Where do you stand now?

[SciFi Chick]

Let's see how this poll stands up after thirty pages of debate. 8)

[Grey]

So far, so good. :D

[Tensor]

Yep.

[worzel]

20% "no's" already :roll:

[SciFi Chick]

20% "no's" already :roll:

Stop being so negative. It's two no's, and we still have two people arguing on the other thread. By contrast, it's 9 yes votes. Give it a little time. :D

[Moose]

Proudly brandishes inky (index) finger. :P

[Edit for clarification. Context is everything. 8) ]

[Glom]

I've helped to move that poll in the right direction.

[Jim]

13-4.

Hey, I'm an engineer. Within 10% is usually close enough. Precision beyond the third decimal is unnecessary and usually wasteful.

[Disinfo Agent]

For the benefit of latecomers to this debate, we should provide them with its context (http://www.badastronomy.com/phpBB/viewtopic.php?t=17953). Let's hope they don't fall asleep half way through the context.

[worzel]

For the benefit of latecomers to this debate, we should provide them with its context (http://www.badastronomy.com/phpBB/viewtopic.php?t=17953). Let's hope they don't fall asleep half way through the context.
It should really be in the OP, and it shoudl say "read this before voting".

26% no's, that's 30% to one significant place, which is almost 1/3, which is the best part of 50%, which if written as 0.5 rounds up to 1, which is a everyone!

[SciFi Chick]

For the benefit of latecomers to this debate, we should provide them with its context (http://www.badastronomy.com/phpBB/viewtopic.php?t=17953). Let's hope they don't fall asleep half way through the context.
It should really be in the OP, and it shoudl say "read this before voting".

26% no's, that's 30% to one significant place, which is almost 1/3, which is the best part of 50%, which if written as 0.5 rounds up to 1, which is a everyone!

Well, do your own poll if you don't like mine. Probably, the only way to be truly accurate is to have each person state their position and someone with time on their hands can add it all up. It's still turning out better than the first poll.

[Disinfo Agent]

It should really be in the OP, and it shoudl say "read this before voting".
But that would be heartless and cruel. :wink:

[jfribrg]

26% no's, that's 30% to one significant place, which is almost 1/3, which is the best part of 50%, which if written as 0.5 rounds up to 1, which is a everyone!

We're at 1/3 or 33.333333...% If we triple the yea votes that will give us 3/3 or 3 x 33.3333333...% or 99.999999999...%


One nagging question: Did we really need another thread on this topic?

[SciFi Chick]

One nagging question: Did we really need another thread on this topic?

If you had finished reading the other thread, you would know the answer to that question.

[Captain Kidd]

I'm afraid to ask (and I don't want to start up that discussion here too), did anybody in the other thread ask about cutting something to such a lenght? If so, what chapter? :)

Being an engineer and not a mathmatician, if somebody can cut me a piece pipe to 26.999999999999999999999... inches and keep it from being 27 inches or 26.99999999...999990 I'll vote no. :D

[edit, edit, and edit again. I'll get this right eventually.]

[Lurker]

I may just vote no because I think we live in a free society and it's extremely fascist to make everyone vote one way!!! [-(

8)

Edited to Add:

Who are the holdouts up there

[worzel]

For the benefit of latecomers to this debate, we should provide them with its context (http://www.badastronomy.com/phpBB/viewtopic.php?t=17953). Let's hope they don't fall asleep half way through the context.
It should really be in the OP, and it shoudl say "read this before voting".

26% no's, that's 30% to one significant place, which is almost 1/3, which is the best part of 50%, which if written as 0.5 rounds up to 1, which is a everyone!

Well, do your own poll if you don't like mine.
Alright, keep your hair on. I thought the point of your pole was to demonstrate your point that many people would have initially voted no and then changed their minds after having read the other thread. After Disinfo's comment it just occurred to me that some people may vote on your pole before realizing there was another thread about it thus enabling you to make the same claim about your pole should it not back up your claim 8-[

[Disinfo Agent]

Poll, not pole. :wink:

[farmerjumperdon]

Yes, because it is in my nature to trust people on topics when they know a lot more about them than I do. Especially when they agree amongst themselves. But not because it makes sense to me. Which it doesn't, but that's only because I am limited by my perspective, part of which is having very limited knowledge of the topic.

Or should I just say, . . . UNCLE! #-o

Thank you.

[Candy]

I voted the same way I voted the last time. ATP is going to give me a lashing. :P

[Disinfo Agent]

Have you read the other thread? :)

[Reacher]

I read that other thread when it was in its infancy, and it convinced me to vote yes, but one thing I don't follow at all is this: Yes. If you don't agree, just ask yourself what you would get if you substracted 9.99999999999999........ from 1.

Why is it that you wouldn't just get -8.99999999....?

I voted for 0.9999r = 0.9999r and 1.0 = 1.0 whatever that means... :D :D :D :D

Isn't the difference between them equal to some kind of infinity...so long as you go to an infinite number of decimal places?? #-o #-o #-o #-o #-o

[SciFi Chick]

Well, do your own poll if you don't like mine.
Alright, keep your hair on. I thought the point of your pole was to demonstrate your point that many people would have initially voted no and then changed their minds after having read the other thread. After Disinfo's comment it just occurred to me that some people may vote on your pole before realizing there was another thread about it thus enabling you to make the same claim about your pole should it not back up your claim 8-[

My hair is on. Don't you worry. :D

Besides, it kind of does still demonstrate my point. The numbers are WAY better on this poll than the last one. I know you won't be happy as long as one person votes the wrong way, but I honestly think this demonstrates that people on this board are willing to change when given new information. It's the reason I love this board. :D

[worzel]

Besides, it kind of does still demonstrate my point. The numbers are WAY better on this poll than the last one.
Yes, I think the results to demonstrate your point.
I know you won't be happy as long as one person votes the wrong way
Well we'll never know now, because we don't know how many voted the wrong way before reading the other thread and changing their minds :P
but I honestly think this demonstrates that people on this board are willing to change when given new information. It's the reason I love this board. :D
I agree.

[Candy]

FWIS, why make fun of the folks who don't except your 'new information' as fact? It doesn't seem nice for some reason. :-?

[jrkeller]

13-4.

Hey, I'm an engineer. Within 10% is usually close enough. Precision beyond the third decimal is unnecessary and usually wasteful.

Unless you're a safety engineer, and then they want precision to the millionth place.

[SciFi Chick]

FWIS, why make fun of the folks who don't except your 'new information' as fact? It doesn't seem nice for some reason. :-?

What are you talking about? Who's making fun of you?

[Candy]

Besides, it kind of does still demonstrate my point. The numbers are WAY better on this poll than the last one. I know you won't be happy as long as one person votes the wrong way, but I honestly think this demonstrates that people on this board are willing to change when given new information. It's the reason I love this board. :D
I guess I should ask you what you mean by what I bolded. To me, from what has already been written that the majority voting for yes are right, and the minority voting for no are wrong. Am I reading to much into 'your' words?

If so, my apologies. FYI, I never said anything was directed at me. :wink:

[tofu]

Can we get 5 more people to vote no, and one more person to vote yes? That would make the totals look like this:

http://seaofcrisis.com/ext/babb/irony.jpg

which would mean that 33.33333... % had voted no, and 66.66666... % had voted yes. And that of course adds up to 99.9999... %

the very definition of irony.

[Lurker]

FWIS, why make fun of the folks who don't except your 'new information' as fact? It doesn't seem nice for some reason. :-?
Well this is a scientific/engineering board. There have been any number of mathematical proofs of this proposition. On the other side, the supposed "proofs" that have been offered to show that the proposition is invalid have been flawed. It's as if Maxwell's equations are rejected even though they have been proven numerous times.

It just seems a bit odd to the rest of us is all.

[SciFi Chick]

Besides, it kind of does still demonstrate my point. The numbers are WAY better on this poll than the last one. I know you won't be happy as long as one person votes the wrong way, but I honestly think this demonstrates that people on this board are willing to change when given new information. It's the reason I love this board. :D
I guess I should ask you what you mean by what I bolded. To me, from what has already been written that the majority voting for yes are right, and the minority voting for no are wrong. Am I reading to much into 'your' words?

If so, my apologies. FYI, I never said anything was directed at me. :wink:

Ah, well, I'm not making fun. Telling someone they're wrong is not my idea of making fun. I happen to think the people voting no are wrong. It's incumbent on those who disagree with established math principles to prove they are right. It's not a philosophical choice. 8)

[Candy]

FWIS, why make fun of the folks who don't except your 'new information' as fact? It doesn't seem nice for some reason. :-?
Well this is a scientific/engineering board. There have been any number of mathematical proofs of this proposition. On the other side, the supposed "proofs" that have been offered to show that the proposition is invalid have been flawed. It's as if Maxwell's equations are rejected even though they have been proven numerous times.

It just seems a bit odd to the rest of us is all.
No offense, Lurker, but there is something missing in this equation. I can’t tell you what it is, because I am not a mathematician. Are you? I don’t study mathematics. I can only tell you that I see something missing.

I do this at work all the time, and I have a hate/love relationship with my boss. He hates when I point him to the flaw in a program. I can’t see the flaw, and I have no idea what the flaw is, but I know this is where I see something missing in the program. My boss is the programmer, so he loves me after he finds the something missing exactly where I pointed it out.

He gives me special projects for just this reason. I’m no Einstein, but I stand by my word and work. FYI, I'm taking my first programming course this session. I'm hoping this will be enough for me to expand on my 'gift' at work. :D

[Candy]

Ah, well, I'm not making fun. Telling someone they're wrong is not my idea of making fun. I happen to think the people voting no are wrong. It's incumbent on those who disagree with established math principles to prove they are right. It's not a philosophical choice. 8)
Perhaps, I will take up 'math principles' after my Masters. :P

[Nicolas]

I searched the web, but nothing useful trurned up. What does "FWIS" mean?

I was think about "Forget What I said" but somehow it does not make sense the way it is used. 8-[

[Lurker]

No offense, Lurker, but there is something missing in this equation. I can’t tell you what it is, because I am not a mathematician. Are you? I don’t study mathematics. I can only tell you that I see something missing.

No offense taken. Mathematics is often not intuitive. The proofs of this proposition that have been offered are pretty basic. In addition limit theory is pretty basic to the foundation of the calculus; so I think you will find most scientists and engineers have known for several hundred years that this proposition is, in fact, true.

You are welcome, however, to take another look.

Um... and when you are finished with this... Somewhere around 550bce there was this guy named Pythagoras of Samos (http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Pythagoras.html). Now he had some rather strange ideas about right triangles...... 8-[

:wink:



Edited because my hyper link didn't come out the first time... :(

[Lurker]

Ah, well, I'm not making fun. Telling someone they're wrong is not my idea of making fun. I happen to think the people voting no are wrong. It's incumbent on those who disagree with established math principles to prove they are right. It's not a philosophical choice. 8)
Scientists and Engineers can be SUCH fascists!! [-(

:wink:

[Candy]

I searched the web, but nothing useful trurned up. What does "FWIS" mean?

I was think about "Forget What I said" but somehow it does not make sense the way it is used. 8-[
It's the forum from the Loresinger website (http://loresinger.com/). There is a link to the FWIS forum, created by Ikyoto, a former BABBer.

[W.F. Tomba]

I slogged a good ways through the other thread, then realized that the discussion was getting less and less enlightening and there were still about 14 pages to go, so I gave up. I'm not going back. The most vocal members of the not-equal camp were mostly just making appeals to "common sense" dressed up in lofty-sounding language. For me, both math and "common sense" say that they are equal.

I was wondering, though, whether anyone actually brought up Zeno's Achilles-vs.-the-tortoise story in the other thread. That's what really seals it for me. If Achilles can catch the tortoise, than it must be possible to add up an infinite number of finite numbers and get a finite sum. The argument that because the decimal is infinitely long, you never quite reach 1 (or in the case of Zeno's Paradox, 100/9) doesn't wash once you think about it in those terms. At least, for me it doesn't.

Let's start a thread about the Cantor set. :wink:

[Candy]

No offense taken. Mathematics is often not intuitive. The proofs of this proposition that have been offered are pretty basic. In addition limit theory is pretty basic to the foundation of the calculus; so I think you will find most scientists and engineers have known for several hundred years that this proposition is, in fact, true.

You are welcome, however, to take another look.
Nope, I'm content on my beliefs. I believe in a future aspect of mathematics that you or I can only imagine. Thank you, anyway.

[Candy]

I searched the web, but nothing useful trurned up. What does "FWIS" mean?

I was think about "Forget What I said" but somehow it does not make sense the way it is used. 8-[
It's the forum from the Loresinger website (http://loresinger.com/). There is a link to the FWIS forum, created by Ikyoto, a former BABBer.
Oops, forgot to add, loresinger is a ~pagan website. FWIS means From Where I Stand.

[Lurker]

Let's start a thread about the Cantor set. :wink:
Its the work of the devil I tell you... the work of the devil!! 8-[

Don't start another battle here... next thing you know we will be arguing over the concept of different radix systems :wink:

[SciFi Chick]

No offense taken. Mathematics is often not intuitive. The proofs of this proposition that have been offered are pretty basic. In addition limit theory is pretty basic to the foundation of the calculus; so I think you will find most scientists and engineers have known for several hundred years that this proposition is, in fact, true.

You are welcome, however, to take another look.
Nope, I'm content on my beliefs. I believe in a future aspect of mathematics that you or I can only imagine. Thank you, anyway.

Well, I hope after you get your Masters and someone comes along and tells you you're wrong about basic business principles because they have a feeling, don't make fun of them by telling them they're wrong. :wink:

[SciFi Chick]

Ah, well, I'm not making fun. Telling someone they're wrong is not my idea of making fun. I happen to think the people voting no are wrong. It's incumbent on those who disagree with established math principles to prove they are right. It's not a philosophical choice. 8)
Scientists and Engineers can be SUCH fascists!! [-(

:wink:

Good thing I'm going to be a mathematician/writer then. :wink:

[Doodler]

As an architecture designer, anything more precise that 1/8" or .125 is considered obnoxious. As a steel worker, I'll occassionally go to 1/16" or .0625, but that's only on some critical assemblies like stairs.

Still, I voted no. Lemme ask y'all this, is a ship moving at .9999999999999~c moving at the speed of light?

[AT]

I don't mean to be hostile when I say this, but am afraid it might sound like it.

This isn't some theoretical, pie-in-the-sky guesswork here; a fairly basic mathimatical fact. It makes me uneasy that there are so many people here willing to argue that its not true.

It makes me very uneasy that there are people on a site for (mostly) debunking bad science that ignore rock-solid mathimatical proofs.

[Moose]

Lemme ask y'all this, is a ship moving at .9999999999999~c moving at the speed of light?

Yes.

[farmerjumperdon]

And I thought I was stubborn. :lol:

[Moose]

This isn't some theoretical, pie-in-the-sky guesswork here; a fairly basic mathimatical fact. It makes me uneasy that there are so many people here willing to argue that its not true.

Agreed. Mathematics is the one scientific field where there's no such thing as "close enough". Estimates have at least some value in physics and engineering. Computing Science has no choice but to estimate and accept "as close as you can encode". Math? Nope. It may be close but it's still wrong.

It's definitely odd to see such resistance, on a science board, to the one field where it's possible to prove something without misusing the term.

[Doodler]

AT, you've got to take in a bit more than the absolute. There are such things as tolerances which allow for a little variation. Those tolerances are critical in construction and engineering, because its not humanly possible in some cases to attain gnat's butt accuracy in the product.

Perfection works in theory, but it doesn't translate well into practice.

[AT]

I'm engineering student, so I love fudge factors. But this is math, where there isn't one (unless the professor is nice). There are exact values in mathimatics. There are none of the tolarances that I love in inductors or capacitors when it comes to Math.

Also, I don't have to spell anything correctly.

[Lurker]

As an architecture designer, anything more precise that 1/8" or .125 is considered obnoxious. As a steel worker, I'll occassionally go to 1/16" or .0625, but that's only on some critical assemblies like stairs.

Still, I voted no. Lemme ask y'all this, is a ship moving at .9999999999999~c moving at the speed of light?

The answer to your question is yes.

What we are discussing here here is not accuracy or precision... it's limit theory. One does not use this sort of mathematics when drilling a hole or fitting elements together. However, if I have a steel beam that's under load it may be necessary to use a differential equation in order to determine the over-turning moment induced by these loads.

The determination of the solution to that differential equation requires the use of the calculus. The Fundamental Theorum of Calculus is built on limit theory. So, if the proposition that we are discussing here is not true, then I cannot use calculus to determine the moment in my beam. If I can't do this then I don't have the tools necessary for the design of modern structures.

I would add, however, that the structural analysis methods based on calculus do in fact produce the correct answers. This IS, in fact, how nature works.

[farmerjumperdon]

Following this thread is fun in a watching-a-car-crash sort of way.

[worzel]

Perfection works in theory, but it doesn't translate well into practice.
And maths is pure theory, right?

[Disinfo Agent]

Following this thread is fun in a watching-a-car-crash sort of way.
Why is that?

[mickal555]

I stopped reading the other thread when I got up the next morning and it was 10 extra pages long. I thought forget it.... and left.
Was Ikyoto a BABBiler... I never knew that... He said something about not being interested in astronomy, and he had never heard of HUb'.

[Disinfo Agent]

Was Ikyoto a BABBiler... I never knew that... He said something about not being interested in astronomy, and he had never heard of HUb'.
Tsk, tsk, tsk... Kids today (http://www.badastronomy.com/phpBB/profile.php?mode=viewprofile&u=2792)! [-(

[Candy]

Ah, well, I'm not making fun. Telling someone they're wrong is not my idea of making fun. I happen to think the people voting no are wrong. It's incumbent on those who disagree with established math principles to prove they are right. It's not a philosophical choice. 8)
Scientists and Engineers can be SUCH fascists!! [-(

:wink:

Good thing I'm going to be a mathematician/writer then. :wink:

All Things Celtic, British, English, Scottish or Irish - Literature, Language and Culture; Science Fiction, Fantasy
You better update your profile, then. One might get or have the impression you don't study math, either. :-"

[farmerjumperdon]

Like a car wreck because of the collision taking place. Pure logic crashing up against common intuition. Both sides certain they are right, bobbing and weaving to avoid damage, but totally irreconcilable in the end; twisted arguements strewn out along the way like so many bits of discarded sheet metal not necessary for basic function but in their absence providing the observer with a glimpse into the workings of what lies beneath. Passerbys gawking, impatient observers honking, and the road workers trying to clear the path.

Every sentence utterred does not need to stand up to the rigors of mathematical proof.

[Disinfo Agent]

Like a car wreck because of the collision taking place. Pure logic crashing up against common intuition.
I wouldn't call it pure logic. There's quite a bit of number theory, algebra, even calculus, in the argument for "0.99... = 1".

Both sides certain they are right, bobbing and weaving to avoid damage, but totally irreconcilable in the end [...]
You think so? I've seen several people in the other thread who started out thinking the two expressions stood for different numbers, but ended up changing their minds. On the other hand, I haven't seen anyone move in the opposite direction.

Every sentence utterred does not need to stand up to the rigors of mathematical proof.
Unless, of course, it happens to be a sentence about mathematical concepts.

[farmerjumperdon]

The nature of your response, picking at each word, says it all. Do you judge a painting by the brushstroke count? My comments were related to behavior, not the merits of either side of the debate; and the sides are irrecncilable, not the people. Oh, no you'ver got me doing it.

[Disinfo Agent]

The two sides are not irreconcilable, as the fact that some people have changed sides clearly shows.

[Candy]

The two sides are not irreconcilable, as the fact that some people have changed sides clearly shows.
On FWIS, I saw a BABBler basically admit to changing sides because he/she didn't want to continue arguing. :o

[Moose]

The nature of your response, picking at each word, says it all.

*sigh* If "not-equal" proponents would provide even a single functional proof, we'd have something more concrete to talk about.

How many times can you rehash the dozen or so distinct proofs before the thread starts to sound like the debunkings over at JREF, or the ones in Against the Mainstream? (I'm frankly surprised that the threads haven't been moved yet.)

[Edited the previous paragraph for coherency.]

Every sentence utterred does not need to stand up to the rigors of mathematical proof.

AT, you've got to take in a bit more than the absolute. There are such things as tolerances which allow for a little variation. Those tolerances are critical in construction and engineering, because its not humanly possible in some cases to attain gnat's butt accuracy in the product.

These statements contain flawed reasoning very similar to that used by proponents of psychic phenomenon and homeopathy. (Yes, really. Take your pick of JREF newsletters for examples.)

Math is not the same as engineering or physics, and it's definitely not the same as philosophy, where it frequently comes down to opinion. There are no tolerances in math. None. No such thing as "close enough". It's either entirely right or it's completely wrong.

[Disinfo Agent]

On FWIS, I saw a BABBler basically admit to changing sides because he/she didn't want to continue arguing. :o
Wow! :o
Why do that, when you can simply leave the discussion, or "agree to disagree"? Plenty have!

P.S. Who was it that did that, and where?

[SciFi Chick]

Ah, well, I'm not making fun. Telling someone they're wrong is not my idea of making fun. I happen to think the people voting no are wrong. It's incumbent on those who disagree with established math principles to prove they are right. It's not a philosophical choice. 8)
Scientists and Engineers can be SUCH fascists!! [-(

:wink:

Good thing I'm going to be a mathematician/writer then. :wink:

All Things Celtic, British, English, Scottish or Irish - Literature, Language and Culture; Science Fiction, Fantasy
You better update your profile, then. One might get or have the impression you don't study math, either. :-"

I don't know if you're trying to be cute or what, but as a matter of fact, this is a recent development, I do need to change my profile, and I'm not on here offering mathematical proofs or asking anyone to change their minds due to the fact I plan to study math. And don't tell me you weren't inferring anything either. Your final comment in that statement says it all.

Edited to Add: Last time I checked, one didn't need a degree in math to comprehend that 1/3 +1/3 + 1/3 = 1.

[SciFi Chick]

On FWIS, I saw a BABBler basically admit to changing sides because he/she didn't want to continue arguing. :o
Wow! :o
Why do that, when you can simply leave the discussion, or "agree to disagree"? Plenty have!

P.S. Who was it that did that, and where?

I'd be interested in that answer as well, since I've reread the thread on this subject at FWIS, and there is no such admission in that thread. Perhaps it is located elsewhere at the site?

[worzel]

Ah, well, I'm not making fun. Telling someone they're wrong is not my idea of making fun. I happen to think the people voting no are wrong. It's incumbent on those who disagree with established math principles to prove they are right. It's not a philosophical choice. 8)
Scientists and Engineers can be SUCH fascists!! [-(

:wink:

Good thing I'm going to be a mathematician/writer then. :wink:

All Things Celtic, British, English, Scottish or Irish - Literature, Language and Culture; Science Fiction, Fantasy
You better update your profile, then. One might get or have the impression you don't study math, either. :-"

I don't know if you're trying to be cute or what, but as a matter of fact, this is a recent development, I do need to change my profile, and I'm not on here offering mathematical proofs or asking anyone to change their minds due to the fact I plan to study math. And don't tell me you weren't inferring anything either. Your final comment in that statement says it all.

Edited to Add: Last time I checked, one didn't need a degree in math to comprehend that 1/3 +1/3 + 1/3 = 1.
You guys aren't going to fall out over something as small as 0.00...01 are you?

[SciFi Chick]

You guys aren't going to fall out over something as small as 0.00...01 are you?

Implications regarding my honesty are not small to me.

[the_shaggy_one]

Being a math major, I answered the question correctly. :P

[farmerjumperdon]

How does the statement "Every sentence utterred does not need to stand up to the rigors of mathematical proof" contain flawed reasoning. It is not even remotely an attempt to reason anything, just a statement that you do not always have to communicate in terms that can be proven mathematically. You can disagree, but to say it is flawed is bizarre. It's like me saying my favorite color is purple, and you telling me the statement is flawed. Oh wait a minute, . . . my favorite color is actually . . . . waaaaaaaaa.

In disagreeing, it is not necessary, or even relevant that the 2 sides agree to do so. By the very nature of disagreement it is by definition obvious the sides disagree, whether they have agreed to disagree or not. Agreeing to disagree is one of those corporate double-speak euphemisms that has crept into everyday use. When someone asks me if we can agree to disagree, I flat out tell them that I disagree with them, whether they want to agree to our disagreement or not.

I don't see an emoticon depicting tongue-in-cheek.

[Moose]

How does the statement "Every sentence utterred does not need to stand up to the rigors of mathematical proof" contain flawed reasoning.

Granted, except we're in a thread about a specific mathematical theorem (or more properly, a counter-claim.) Perhaps it was unreasonable of me, but I did not consider the possibility that future hypothetical statements about your favorite color(s) would be of any real relevance to whether 1 = 0.999r. Or is this a case of "when in doubt, change the subject"?

I do maintain, however, that it is quite necessary for all claims pertaining to the mathematical theorem under discussion must stand up to the rigors of mathematical proof.

[Lurker]

I am not sure exactly what we are suppose to make of those who disagree with the equality proposition being discussed here. One may disagree with the proposition that by sailing west from the California coast one can plot a course that will eventually lead to New York city because one believes the earth is flat. The world however is round. This fact does not change no matter how many polls or disagreements arise over the truth of the proposition. One may choose to disagree with Maxwell's equations, however, they are provably correct as can be seen by any number of applications in our modern technological society.

I am sure that I will get in to no end of trouble for making this final statement on the subject, but I really don't see how this discussion is different from other discussions here that have centered on other woo woo issues. Neal Armstrong did set foot on the moon, the earth is not flat, and the equality proposition being discussed here is well known to be true. No amount of discussion can alter these facts. Whether someone chooses to believe these facts is, as we have seen, a matter of personal choice. But facts do not change to suit personal taste.

[SciFi Chick]

I am sure that I will get in to no end of trouble for making this final statement on the subject, but I really don't see how this discussion is different from other discussions here that have centered on other woo woo issues. Neal Armstrong did set foot on the moon, the earth is not flat, and the equality proposition being discussed here is well known to be true. No amount of discussion can alter these facts. Whether someone chooses to believe these facts is, as we have seen, a matter of personal choice. But facts do not change to suit personal taste.

That comparison came to my mind as well, so if you're in trouble now, we may as well be there together.

[worzel]

I am not sure exactly what we are suppose to make of those who disagree with the equality proposition being discussed here. One may disagree with the proposition that by sailing west from the California coast one can plot a course that will eventually lead to New York city because one believes the earth is flat. The world however is round. This fact does not change no matter how many polls or disagreements arise over the truth of the proposition. One may choose to disagree with Maxwell's equations, however, they are provably correct as can be seen by any number of applications in our modern technological society.

I am sure that I will get in to no end of trouble for making this final statement on the subject, but I really don't see how this discussion is different from other discussions here that have centered on other woo woo issues. Neal Armstrong did set foot on the moon, the earth is not flat, and the equality proposition being discussed here is well known to be true. No amount of discussion can alter these facts. Whether someone chooses to believe these facts is, as we have seen, a matter of personal choice. But facts do not change to suit personal taste.
I would go further, all of your examples could possibly be false. Maxwell's equations may not be exactly right, maybe the earth is flat afterall and it's just our limited perception that makes it indistinguishable from a near sphere to us, etc. etc. But whatever may be thought to be true or false about the universe, we can be sure that 0.99..=1, just like we can be sure that 2+2=4.

[Lurker]

I am sure that I will get in to no end of trouble for making this final statement on the subject, but I really don't see how this discussion is different from other discussions here that have centered on other woo woo issues. Neal Armstrong did set foot on the moon, the earth is not flat, and the equality proposition being discussed here is well known to be true. No amount of discussion can alter these facts. Whether someone chooses to believe these facts is, as we have seen, a matter of personal choice. But facts do not change to suit personal taste.

That comparison came to my mind as well, so if you're in trouble now, we may as well be there together.
So when we get banned... will you be my friend?? :(

[SciFi Chick]

I am sure that I will get in to no end of trouble for making this final statement on the subject, but I really don't see how this discussion is different from other discussions here that have centered on other woo woo issues. Neal Armstrong did set foot on the moon, the earth is not flat, and the equality proposition being discussed here is well known to be true. No amount of discussion can alter these facts. Whether someone chooses to believe these facts is, as we have seen, a matter of personal choice. But facts do not change to suit personal taste.

That comparison came to my mind as well, so if you're in trouble now, we may as well be there together.
So when we get banned... will you be my friend?? :(

We won't get banned. We're not being mean. However, if I happen to be wrong, you will just have to come over to FWIS. And I'm your friend now.

[Frog march]

perhaps the NO voters are all German and are saying to them selves,
"Nein, nein, nein, nein, nein, nein, nein..........................." :wink:

[Lurker]

I am sure that I will get in to no end of trouble for making this final statement on the subject, but I really don't see how this discussion is different from other discussions here that have centered on other woo woo issues. Neal Armstrong did set foot on the moon, the earth is not flat, and the equality proposition being discussed here is well known to be true. No amount of discussion can alter these facts. Whether someone chooses to believe these facts is, as we have seen, a matter of personal choice. But facts do not change to suit personal taste.

That comparison came to my mind as well, so if you're in trouble now, we may as well be there together.
So when we get banned... will you be my friend?? :(

We won't get banned. We're not being mean. However, if I happen to be wrong, you will just have to come over to FWIS. And I'm your friend now.

I appreciate it too... when I got buried by life and work a while back you were asking what happened to lurker on the missing posters thread... :)

[SciFi Chick]

I appreciate it too... when I got buried by life and work a while back you were asking what happened to lurker on the missing posters thread... :)

Then I got buried about the time you responded. I'm on Spring Break at the moment, which is why I'm around.

[gethen]

Page four of a poll about a topic already discussed for 30 pages. Some people just have too much time on their hands. :wink:

[R.A.F.]

Some people just have too much time on their hands. :wink:

Now I don't think that...

So where do I stand?? At the moment at 39' 48.43" N, by 121' 34.70" W.

(give of take 50 meters. :))

[worzel]

Page four of a poll about a topic already discussed for 30 pages. Some people just have too much time on their hands. :wink:
I don't know how much time you have on your hands, but I don't enough time to go round reading threads I'm not interested in and then posting about what a waste of time they are :)

[Candy]

On FWIS, I saw a BABBler basically admit to changing sides because he/she didn't want to continue arguing. :o
Wow! :o
Why do that, when you can simply leave the discussion, or "agree to disagree"? Plenty have!

P.S. Who was it that did that, and where?

I'd be interested in that answer as well, since I've reread the thread on this subject at FWIS, and there is no such admission in that thread. Perhaps it is located elsewhere at the site?
Here it is! (http://loresinger.com/FWIS/viewtopic.php?p=21553#21553) Basically, the poster just gave "in", because of the arguing. :D

[Normandy6644]

Wow, I must have missed this thread earlier! Four pages already! Too many "no's" for my liking though... :-?

[Disinfo Agent]

On FWIS, I saw a BABBler basically admit to changing sides because he/she didn't want to continue arguing. :o
Wow! :o
Why do that, when you can simply leave the discussion, or "agree to disagree"? Plenty have!

P.S. Who was it that did that, and where?

I'd be interested in that answer as well, since I've reread the thread on this subject at FWIS, and there is no such admission in that thread. Perhaps it is located elsewhere at the site?
Here it is! (http://loresinger.com/FWIS/viewtopic.php?p=21553#21553) Basically, the poster just gave "in", because of the arguing. :D
Who was the poster?

[gethen]

Page four of a poll about a topic already discussed for 30 pages. Some people just have too much time on their hands. :wink:
I don't know how much time you have on your hands, but I don't enough time to go round reading threads I'm not interested in and then posting about what a waste of time they are :)
Yep. Guilty as charged.

[Grey]

Who was the poster?
Looks like herself. Just from the posts, it's not really certain that's the reason she gave in, but I'll trust Candy to know her own mind. :D

[Candy]

Who was the poster?
Looks like herself. Just from the posts, it's not really certain that's the reason she gave in, but I'll trust Candy to know her own mind. :D
I gave "in" by compromising.

No, you guys did a fine job. I will rephrase my statement, I understand the answer will ultimately equal 1 with a process of calculations (or should I say equations).

What they kept giving me as proof is proof to what they want the answer to be, in this case, 1. It was the same examples over and over and over.

I don't think the posters fully understand where I was coming from or what I was saying, so I had to gracefully leave the thread before my head burst. I’ll probably have to do that on this thread, as well. :wink:

[Grey]

What they kept giving me as proof is proof to what they want the answer to be, in this case, 1. It was the same examples over and over and over.

I don't think the posters fully understand where I was coming from or what I was saying, so I had to gracefully leave the thread before my head burst. I’ll probably have to do that on this thread, as well. :wink:
I won't insist on discussing it further if you'd prefer, but I'd like to try to illuminate a few things. It's certainly true that many people restated the same or similar proofs that 0.999... = 1. Since all the proofs are attempting to demonstrate the same thing, it's expected that they'll have some similarity in form.*

I think the hope is that by phrasing it in a different manner, it might be more clear or persuasive. I've found that to be the case when teaching Renaissance dance. When there are some tricky elements, I often have several different ways of explaining the same pattern, and some people get it better one way, while for another person that way of explaining it just confuses them more. But if I explain the pattern in a different way, it makes sense to that person.

Anyway, I'd like to address your comment that you think someday someone will develop a new mathematics, that will show why 0.999... = 1 isn't true. I'd like to show why I don't think this can happen, since mathematics isn't something we discover, it's something we create. I'll use an analogy, if I may.

Let's liken the statement in question to the statement "the interior angles of a triangle add up to 180 degrees". Now, at first, it might not be obvious whether this is true or not, and you might imagine that it might be true, or false, or even true for some triangles but not for others. But a little exploration into geometry shows that, relying only on the axioms of geometry, we can show that this is always true for any triangle. So, actually, inherent in what we mean when we talk about a triangle is an object whose interior angles add up to 180 degrees, even if we didn't realize it at first. It's as much a part of being a triangle as having three sides is, it's just not quite as obvious. In the same way, the basic axioms that we use to define what real numbers are (and remember, we're the ones who decided what they are, rather than trying to figure out what they are, like determining that protons are made out of quarks) can be used to show that 0.999... = 1.

"But wait," you say, "someone could come up with some other mathematics that shows they aren't equal." And in fact, one might say that's true of the triangle case, too. It turns out, after years of mathematicians trying to prove the Euclid's fifth postulate using just the first four, that it can't be done. One of the implications of that is that it's possible to have a self-consistent geometry where the interior angles of a triangle always add up to less than 180 degrees, or one where they always add up to more than 180 degrees. This was pretty shocking when it was realized, and the familiar terms like points and lines don't have to mean quite what we thought they meant in these new geometries.

The thing is, though, that those are distinct geometries. They have their uses (and with the advent of general relativity, we realized that it might be that the real universe actually follows one of these other geometries, rather than the Euclidean one that we always assumed), and they're fun for mathemeticians to play with. But Euclidean geometry itself isn't affected by this realization! That is, in Euclidean geometry triangles are always the same as they have been, and if we come up with yet a new geometry, that still won't change. And we still use Euclidean geometry all the time (explicitly, when doing mathematics, and implicitly, when doing things like building houses or making furniture). Most people never even realize that the geometry they learned in school is only one of several possible consistent geometries, in fact.

In the same way, it might be possible to come up with a self-consistent number system in which 0.999... does not equal 1. Such a system might involve infinitesimals, or hyperreal numbers, or something more esoteric, and the fact that I have names that I can assign some of the possibilities should suggest that mathematicians have already been playing with such concepts.

However (and here's my point after all this talking :) ), these number systems aren't the real numbers. And it's not ever likely that they'll replace the real number system either, any more than we would start teaching non-Euclidean geometry to elementary school children. They'll remain systems that advanced mathematicians play with, and generally, while those mathematicians could in principle choose to use a notation system that would make these symbols look like they might be real numbers, they generally choose not to do so, specifically because of the confusion that might be engendered.

So someone might develop an unusual self-consistent number system, and choose a notation system such that the symbols 0.999... and 1 are meaningful numerals that do not in fact represent the same value. But if they did so, those symbols wouldn't have quite the same meaning as those symbols have in the real number system. So creating such a system wouldn't change the truth of the statement many have made here, that within the system of real numbers, 0.999... = 1, any more than the creation of non-Euclidean geometries changes the fact that in the geometry we usually use by default the interior angles of a triangle still add up to 180 degrees.

* My personal favorite is the one using 0.333... = 1/3, and then multiplying by 3, since that doesn't involve limit theory. While the result ultimately depends on limits, it seems that everyone who disagrees with the statement seems to do so out of an intuitive sense that it can't be true. So it's important to make the proof as clear and natural as possible, to appeal to that same intuition, if you want to convince someone. A more formal proof may be rigorous, but you lose the audience.

[Lurker]

After so many pages of discussion on this I am going to just have to excuse myself from what has simply become another woo woo discussion. The woo woos who are not convinced at this point are not interested in the facts and it does no good running through the proofs again and again.



edited for grammar

[Disinfo Agent]

After so many pages of discussion on this I am going to just have to excuse myself from what has simply become another woo woo discussion. The woo woos who are not convinced at this point are not interested in the facts and it does no good running through the proofs again and again.
Definitely not in this thread. But I wouldn't say that the "doubters" are being woo-woo. This is simply a case of misconceptions or a superficial understanding of a subject causing "intuition" to conflict with rigorous thought. Most people are hesitant to let go of what their intuition tells them, understandably. And sometimes new ideas just take some time to sink in.

I would like to add one comment to Grey's excellent post. Even today, some conventional mathematicians are uncomfortable with this quirk of our place-value numbering system that allows some real numbers to have two different representations. In some technical works, you will find that the authors prefer to leave repeating decimals ending in "999..." undefined. For them, the symbol "0.999..." simply does not represent a number (in base 10).

This is always a valid way out, but of course it evades the question of what meaning, if any, should be given to such numerals. So, within current conventional mathematics, there are two possible choices: either accepting that "1" and "0.999..." stand for the same number, or refusing to assign any meaning whatsoever to one of those expressions.

[Candy]

I think the hope is that by phrasing it in a different manner, it might be more clear or persuasive. I've found that to be the case when teaching Renaissance dance. When there are some tricky elements, I often have several different ways of explaining the same pattern, and some people get it better one way, while for another person that way of explaining it just confuses them more. But if I explain the pattern in a different way, it makes sense to that person.
I understand this. I tutored others in Algebra and Calculus during my Ball State daze. I used the same teaching pattern.

Anyway, I'd like to address your comment that you think someday someone will develop a new mathematics, that will show why 0.999... = 1 isn't true. I'd like to show why I don't think this can happen, since mathematics isn't something we discover, it's something we create. I'll use an analogy, if I may.
Then I’ll rephrase my statement, and replace my discover verbiage with create verbiage.

So someone might develop an unusual self-consistent number system, and choose a notation system such that the symbols 0.999... and 1 are meaningful numerals that do not in fact represent the same value. But if they did so, those symbols wouldn't have quite the same meaning as those symbols have in the real number system. So creating such a system wouldn't change the truth of the statement many have made here, that within the system of real numbers, 0.999... = 1, any more than the creation of non-Euclidean geometries changes the fact that in the geometry we usually use by default the interior angles of a triangle still add up to 180 degrees.
I understand what you are saying, and I’m okay with the fact that in this world at this “moment” in time, 0.999… equals 1. I get your thinking. I get your analogies. Seriously, I get it.

I don’t agree that it is equal [now or] on a 'future creative' level. Why is my way of thinking so totally incomprehensible to many? Now, that I don’t get.

[Edited to add a couple of words.] :D

[Frog march]

the NOers make the mistake in thinking that their intuition is familiar with the infinite.

edited for spelling

[Lurker]

I don’t agree that it is equal [now or] on a 'future creative' level. Why is my way of thinking so totally incomprehensible to many? Now, that I don’t get.

Your way of thinking is not at all incomprehensible. It's simply wrong. It is as wrong as the statement, "Neal Armstrong never walked on the moon", and it is being treated as such. I don't understand why that bothers you. This is a scientific forum and the equality proposition under discussion is provably true. You may believe as you wish; no one has any interest in Interfering with that. However, the simple and undeniable fact remains; you are wrong.

[Candy]

the NOers make the mistake in thinking that their intuition is familiar with the infinite.

edited for spelling
Don't you ever get that feeling when you look at something, that there's something missing? You can't quite put your finger on it, but there's something missing? I don't believe this is what you refer to as intuition in my case, do you? 8-[

I created a theorem during a freshman calculus course back in the mid 80's that worked ~99.7% of the time, and it was easier for students to understand. The professor purposely changed the final exam, because I told him what I was working on. I almost flunked the exam due to this idiotic attitude the professor had that today's math is what should be accepted. I loved math, but after meeting a very closed minded professor, I stopped being interested in it. At the time, this was a class I chose as an elective. I was planning on minoring in math. :(

[Disinfo Agent]

I understand what you are saying, and I’m okay with the fact that in this world at this “moment” in time, 0.999… equals 1. I get your thinking. I get your analogies. Seriously, I get it.

I don’t agree that it is equal [now or] on a 'future creative' level. Why is my way of thinking so totally incomprehensible to many? Now, that I don’t get.
I'm sorry, Candy, but in one paragraph you write 'I’m okay with the fact that in this world at this “moment” in time, 0.999… equals 1', and in the very next one you write 'I don’t agree that it is equal [now or] on a 'future creative' level'.

What are we to make of this?

[Candy]

I understand what you are saying, and I’m okay with the fact that in this world at this “moment” in time, 0.999… equals 1. I get your thinking. I get your analogies. Seriously, I get it.

I don’t agree that it is equal [now or] on a 'future creative' level. Why is my way of thinking so totally incomprehensible to many? Now, that I don’t get.
I'm sorry, Candy, but in one paragraph you write 'I’m okay with the fact that in this world at this “moment” in time, 0.999… equals 1', and in the very next one you write 'I don’t agree that it is equal [now or] on a 'future creative' level'.

What are we to make of this?
I understand what Grey is saying, and I understand his logic. I should have said I'm okay with the fact that in this world at this "moment" in time, 0.999... equals 1 [to you]. My bad. I just don't agree or believe that it does.

And as Lurker so rudely stated, "you are wrong". Nice way of communicating. You wonder why [23% - see results] of people don't actually state the way they feel sometimes on this board. :roll:

[Grey]

I understand what you are saying, and I’m okay with the fact that in this world at this “moment” in time, 0.999… equals 1. I get your thinking. I get your analogies. Seriously, I get it.
Alas, I'm not certain that you do, since the point was that the statement isn't about what's true at this moment in time, that might have been different in the future or the past. It's a statement about what will always be true. If I take the statement 2+2=4, but then I redefine my symbols, so what I use to call "3", I now write as "2", and vice versa, I should now write 2+2=6. But while that appears to be contradicting the previous statement, it isn't, because although the symbols on the left look the same, they've been redefined to mean something different.

Don't you ever get that feeling when you look at something, that there's something missing? You can't quite put your finger on it, but there's something missing? I don't believe this is what you refer to as intuition in my case, do you? 8-[
Um, I'm afraid that's exactly what I'd call intuition.

I created a theorem during a freshman calculus course back in the mid 80's that worked ~99.7% of the time, and it was easier for students to understand. The professor purposely changed the final exam, because I told him what I was working on. I almost flunked the exam due to this idiotic attitude the professor had that today's math is what should be accepted. I loved math, but after meeting a very closed minded professor, I stopped being interested in it. At the time, this was a class I chose as an elective. I was planning on minoring in math. :(
Well, the professor may not have handled things the best way, but a "theorem" that works 99.7% of the time isn't a theorem in mathematics. Maybe it's a "rule of thumb", or a "guideline" (arrrg, matey!) and might be useful in some cases, but pure mathematics is all about rigorous proof. I'm sorry that you're no longer interested in math, but perhaps given your views it was inevitable that you'd have been dissatisfied with it at some point regardless. I'm curious, though. Can you remember far enough back to recall the details?

[SciFi Chick]

And as Lurker so rudely stated, "you are wrong". Nice way of communicating. You wonder why [23% - see results] of people don't actually state the way they feel sometimes on this board. :roll:

Telling someone they are wrong when they are in fact wrong is not rude. I'm sorry hearing the truth offends you, but that does not make stating the truth rude.

[Candy]

Alas, I'm not certain that you do, since the point was that the statement isn't about what's true at this moment in time, that might have been different in the future or the past. It's a statement about what will always be true. If I take the statement 2+2=4, but then I redefine my symbols, so what I use to call "3", I now write as "2", and vice versa, I should now write 2+2=6. But while that appears to be contradicting the previous statement, it isn't, because although the symbols on the left look the same, they've been redefined to mean something different.
It's useless, you won't convince me. The only way I would answer yes to the question posed is if it were worded differently. Since you are starting to understand me, can you guess how it should be worded?

Um, I'm afraid that's exactly what I'd call intuition.
I think of intuition as when you know something's going to happen. So I guess you are right in this case. :wink:

Well, the professor may not have handled things the best way, but a "theorem" that works 99.7% of the time isn't a theorem in mathematics. Maybe it's a "rule of thumb", or a "guideline" (arrrg, matey!) and might be useful in some cases, but pure mathematics is all about rigorous proof. I'm sorry that you're no longer interested in math, but perhaps given your views it was inevitable that you'd have been dissatisfied with it at some point regardless. I'm curious, though. Can you remember far enough back to recall the details?
I was so mad at the professor that I told him to use it as his own. I can't remember the details now. I was ~19. If I'd only known about the BABB then, I would've saved everything. The professor bragged that he was related to Sir Isaac Newton, though.

[Grey]

It's useless, you won't convince me. The only way I would answer yes to the question posed is if it were worded differently. Since you are starting to understand me, can you guess how it should be worded?
Hmm, I'll try to come up with a version that you might agree with, but which still preserves the essence of the mathematical statement, as far as I'm concerned. How about this:

The number represented by the numeral 0.999..., as defined within the system of real numbers, has the same value as the number defined by the numeral 1, also as defined within the system of real numbers.

Oh, and I think you misattributed one of those quotes. :D

[Disinfo Agent]

I understand what Grey is saying, and I understand his logic. I should have said I'm okay with the fact that in this world at this "moment" in time, 0.999... equals 1 [to you]. My bad. I just don't agree or believe that it does.
Why is my way of thinking so totally incomprehensible to many? Now, that I don’t get.
In the other thread, several proofs of the equality 0.999...=1 were presented, and no proof that it isn't true was ever produced (obviously). Given that we have ways of showing that a statement is true, shouldn't we accept that it is indeed true?

Considering all the proofs in favor of the equality that have been put forth, I see only four possibilities:

1) Either the proofs are correct, and then it seems that you should believe what they say.
2) Or you did not understand any of the proofs. We can try to explain them better, if that's the case.
3) Or all the proofs contained errors--but where are those errors? No one's identified any so far.
4) Or the proofs are correct, but they're based on definitions which you feel are not the best. Then you should try to explain what is your definition of the relevant concepts (like that of decimal numeral), how it's different from the one we're using, and why it's preferable to ours.

[Candy]

Hmm, I'll try to come up with a version that you might agree with, but which still preserves the essence of the mathematical statement, as far as I'm concerned. How about this:

The number represented by the numeral 0.999..., as defined within the system of real numbers, has the same value as the number defined by the numeral 1, also as defined within the system of real numbers.
I was thinking more like...

do you think this statement is true...

1/3 + 1/3 + 1/3 = 3/3

then do you think this statement is true...

3/3 = 1

then do you think...

1/3 = .333...

I would then answer yes up to this point.

If the above statement is true, then...

.333... + .333... + .333... = 1

is true. [YOU MUST BELIEVE. We can prove it scientically.]

This I would not agree with. :wink:

Oh, and I think you misattributed one of those quotes. :D
I learn from the best. :lol:

[Grey]

This I would not agree with. :wink:
I take it, then, that you disagree with the principle that if two values are equal, then one can be substituted for the other in any equation in which it appears?

[Captain Kidd]

I was thinking more like...

do you think this statement is true...

1/3 + 1/3 + 1/3 = 3/3

then do you think this statement is true...

3/3 = 1

then do you think...

1/3 = .333...

I would then answer yes up to this point.
0.333... is only an approximation of 1/3. 1/3 is a number that cannot be represented fully decimially as it has no end.


If the above statement is true, then...

.333... + .333... + .333... = 1

is true. [YOU MUST BELIEVE. We can prove it scientically.]

This I would not agree with. :wink:

I cannot agree.

1/3 + 1/3 + 1/3 = 3/3 = 1.

0.333... + 0.333... + 0.333... is only the sumations of decimal representations of 1/3.

Therefore, it adds up to 1.

[edit and edit to finally get it to say what I mean.]

[Candy]

This I would not agree with. :wink:
I take it, then, that you disagree with the principle that if two values are equal, then one can be substituted for the other in any equation in which it appears?
From FWIS, I believe the issue I had was the ... (finite or infinite). I gave it a value, when others simply dismissed it having a value.

[Disinfo Agent]

0.333... is only an approximation of 1/3.
What does "0.333..." mean to you? A zero followed by a point and three threes?

[Captain Kidd]

0.333... is only an approximation of 1/3.
What does "0.333..." mean to you? A zero followed by a point and three threes?

In my earlier post it was a zero followed by a decimal point followed by infinite 3's.

In calculations I'd use as many 3's as the significant digit rule called for, or for more accurace 1/3.

[edit I cannot spell today.]

[Disinfo Agent]

In my earlier post it was a zero followed by a decimal point followed by infinite 3's.
In that case, what you wrote was false. It's not just an approximation; it is 1/3.

[Candy]

0.333... is only an approximation of 1/3. 1/3 is a number that cannot be represented fully decimially as it has no end.
This is what I am talking about! What if you have .333... from one spot in time and add it to another .333... from another point in time and then add it to another .333...?

Each .333... can not represent a perfect third of each other.

One of the .333... has to have a value greater than, less than, or equal to 1/3.!
(Sorry, I had to use an exclamation point to distinguish the points.)

Do you see my funky way of thinking, yet? 8-[

[sorry, had to edit twice]

[Grey]

From FWIS, I believe the issue I had was the ... (finite or infinite). I gave it a value, when others simply dismissed it having a value.
I think that the most common problem with working with infinity is assuming that it's some really large value. But if this were your problem, I would think that you'd disagree with the statement 0.333... = 1/3. If you accept that those two are equal, as you suggested, then I think you have to deny either the axiom that two things that are both equal to a third are equal to each other, or else deny standard logic in order to escape the conclusion.

[AT]

What if I use algebra?

3X =1

Solve

X=1/3

1/3 = 0.333333333.....

Therefore,

3*(0.33333.....) = 1.

Why does your feelings that 'this doesn't seem right' trump the proof that it is?

[Captain Kidd]

In my earlier post it was a zero followed by a decimal point followed by infinite 3's.
In that case, what you wrote was false. It's not just an approximation; it is 1/3.

And in that case 0.999... (zero point infinite nines) is 3/3 which is 1.

[Grey]

One of the .333... has to have a value greater than, less than, or equal to 1/3.!
(Sorry, I had to use an exclamation point to distinguish the points.)

So you're assuming that 0.333... actually refers to more than one number. That is, specifying a decimal expansion does not uniquely define a number as far as you're concerned. I would still think this would mean that you'd disagree with the statement 0.333... = 1/3, or at least you'd want to put a caveat on it, that it's only sometimes equal. Are you certain that if you allow that to be true that the notion of equality still has any meaning at all in the number system you're proposing?

[Candy]

One of the .333... has to have a value greater than, less than, or equal to 1/3.!
(Sorry, I had to use an exclamation point to distinguish the points.)

So you're assuming that 0.333... actually refers to more than one number. That is, specifying a decimal expansion does not uniquely define a number as far as you're concerned. I would still think this would mean that you'd disagree with the statement 0.333... = 1/3, or at least you'd want to put a caveat on it, that it's only sometimes equal. Are you certain that if you allow that to be true that the notion of equality still has any meaning at all in the number system you're proposing?
Do you mean I'm thinking that the value 0.333... is actually [derived] from multiple number 1's? Then yes.

sorry - had to edit

[AT]

Do you mean I'm thinking that the value 0.333... is actually from multiple numbers? Then yes.

Its not; if it were a function, each decimal 'x' value has one, and only one, simplified fraction 'y' value.

[Grey]

I can't remember the details now. I was ~19. If I'd only known about the BABB then, I would've saved everything.
Too bad. Of course, the BABB wouldn't have been nearly as interesting a place back then, since even the Bad Astronomer hadn't joined yet. You and Colt would have been the only members. Still, poor Colt would have had 14 fewer years to wait around for someone to talk to. :D

[Grey]

Do you mean I'm thinking that the value 0.333... is actually [derived] from multiple number 1's? Then yes.
That would suggest to me that you don't necessarily think these equations are always true:

0.333... = 0.333...

1 = 1

Is that correct?

[Lurker]

And as Lurker so rudely stated, "you are wrong". Nice way of communicating. You wonder why [23% - see results] of people don't actually state the way they feel sometimes on this board. :roll:
It's unfortunate that you feel my comment was rude. I was never my intention of being rude to you Candy; I consider you to be my friend. That being said, the proposition being discussed in this thread is a well known, provable fact. I had thought that in a scientific forum such as this, such issues would not be taken personally.

[Candy]

Do you mean I'm thinking that the value 0.333... is actually from multiple numbers? Then yes.

Its not; if it were a function, each decimal 'x' value has one, and only one, simplified fraction 'y' value.
I don't understand what you mean.

I think this is why I'm not getting this to add up to 1.

I believe there is a value associated to ...

So if you take 0.333... from one perfect 1/3 of 1 and add it to another perfect 1/3 and so on, it may eventually add up to 1 (but chances are slim).

There has to be an end point for that perfect 1/3 ... to level off to a side. Who are we to decide what that ... will be? :-?

[Candy]

Do you mean I'm thinking that the value 0.333... is actually [derived] from multiple number 1's? Then yes.
That would suggest to me that you don't necessarily think these equations are always true:

0.333... = 0.333...

1 = 1

Is that correct?
When you write it like that, then I would say yes all values are equal.

But now, I'm not so sure about the 0.333... = 0.333...

You boys have opened my eyes to yet another possibility. :D

[jfribrg]

I haven't read all of the threads (will never have that much time), but I just thought of another way of explaining it. There are only so many ways of saying the same thing, so it's probably been stated before, but in case it hasn't, I weill state it now.

It's not really a rigorous proof, but since the rigorous proofs given many different ways in these threads still leave a few folks unconvinced ](*,) , maybe a not so rigorous explanation will help.

Between any two different real numbers, there are an (uncountably) infinite number of real numbers between them. The only way that they can have no real numbers between is if they are both the same number. Since 0.999999... and 1 don't have any numbers between them, they must not be different.

I think the main stumbling block for some folks is the notion that the 9's have to stop at some point, when in fact they don't stop.

[Grey]

I believe there is a value associated to ...
I think that you may be ascribing more to that ellipsis than just an indication that the sequence continues indefinitely.

Who are we to decide what that ... will be? :-?
Well, we are the ones to decide, remember? That is, not necessarily each of us individually, but as a group of mathematicians (I'm giving us the benefit of the doubt :D ) if we're going to use a symbol, we need to figure out precisely what it's going to mean, and then use it consistently.

But now, I'm not so sure about the 0.333... = 0.333...
If I may, I'd like to ask again. Do you think you can have a consistent system where this isn't always true and still have equality be a meaningful concept?

[Candy]

Who are we to decide what that ... will be? :-?
Well, we are the ones to decide, remember? That is, not necessarily each of us individually, but as a group of mathematicians (I'm giving us the benefit of the doubt :D ) if we're going to use a symbol, we need to figure out precisely what it's going to mean, and then use it consistently.
Perhaps, this is why string theory is just that... a theory. :-k

But now, I'm not so sure about the 0.333... = 0.333...
If I may, I'd like to ask again. Do you think you can have a consistent system where this isn't always true and still have equality be a meaningful concept?
Yes. Do I know how? No. I leave that for the 'future' mathematicians. :wink:

[Grey]

Perhaps, this is why string theory is just that... a theory. :-k
I'm not really certain that follows. String theory works out well mathematically, though the details are pretty complex. The reason it's a theory (and still a pretty untried one at that) isn't because of a problem with the mathematics. It's that it's being proposed as a model of how the universe actually works. Now there's a question of whether the mathematical model we've created actually corresponds to something in nature, and that's a question that can only be answered by experiment. We've just crossed the lin efrom mathematics into physics.

Yes. Do I know how? No. I leave that for the 'future' mathematicians. :wink:
If you're uncertain that 0.333... = 0.333..., why aren't you questioning whether 1 = 1? Or what about 1.000... = 1.000...? That sounds again like you're suggesting that "..." can have different "values", apart from just signifying that the sequence should continue. But does it really make sense to you that the same symbols should represent different things? Since we were the ones who defined what those symbols meant, why would we do that?

[Captain Kidd]

In my earlier post it was a zero followed by a decimal point followed by infinite 3's.
In that case, what you wrote was false. It's not just an approximation; it is 1/3.

And in that case 0.999... (zero point infinite nines) is 3/3 which is 1.
I thought it over on the drive home and I think I get what you're driving at. (err, no pun intended.)

I said 0.333... is an approximation of 1/3. Then I said the terminology I used meant infinite 3's after the decimal point. However, I now see where I erred. Those are mutually exclusive statements. Infinite 3’s behind a decimal is 1/3.

So...
1/3 = 0.333...
Therefore:
1/3 + 1/3 + 1/3 = 0.333... + 0.333... + 0.333... = 0.999... which equals 3/3 and thus 1.

Had that first post declared a finite number of threes, no matter how many, then it’d have been correct to state it was an approximation.

[Disinfo Agent]

You got it. :D

If you stopped at 0.3, you'd have an approximation to 1/3 with a positive error less than 0.1. If you stopped at 0.333, you'd have an approximation to 1/3 with a positive error less than 0.001. Even if you stopped only at 0.3333333333333333333333, you'd still have a positive error, though less than 0.0000000000000000000001. But if you don't stop, the error is zero. :)

[Moose]

Right. The whole point of 0.999... as notation isn't that we're approximating the value of an infinite series of decimalled nines. We're approximating the visual representation of an infinite series of decimalled nines to make working with it possible. The value itself is unchanged. It's still exactly equal to 1, just like 1/3 is exactly equal to the value that the symbol 0.333... represents.

[Captain Kidd]

You got it. :D

If you stopped at 0.3, you'd have an approximation to 1/3 with a positive error less than 0.1. If you stopped at 0.333, you'd have an approximation to 1/3 with a positive error less than 0.001. Even if you stopped only at 0.3333333333333333333333, you'd still have a positive error, though less than 0.0000000000000000000001. But if you don't stop, the error is zero. :)

I blame it on age, wait I'm 28 (for 5 more days). Hmm, that won't work... Ok, sleep depravation! Yeah that's it!

[Lurker]

I blame it on age, wait I'm 28 (for 5 more days). Hmm, that won't work... Ok, sleep depravation! Yeah that's it!

I can blame things on age... YOU at 28 cannot!! [-(

:wink:

[Frog march]

what about this problem in another number base like base 5 ie the equivelant would be 0.444444444444444........... or in hexidecimal then the equivelant would be 0.FFFFFFFFFFFFFFF........... the same rule should apply although i dont know about base 2's 0.111111111111....... maybe that too is ONE.....!!! Im not sure...

[Disinfo Agent]

Yep, it's 1. :)
Bases other than 10 were discussed extensively in the thread over at FWIS (http://loresinger.com/FWIS/viewtopic.php?p=21313#21313).

[Candy]

If you're uncertain that 0.333... = 0.333..., why aren't you questioning whether 1 = 1? Or what about 1.000... = 1.000...? That sounds again like you're suggesting that "..." can have different "values", apart from just signifying that the sequence should continue. But does it really make sense to you that the same symbols should represent different things? Since we were the ones who defined what those symbols meant, why would we do that?
It's those ...'s that bother me. 8-[

Ok, off to class. I'm so tired right now. :-?

[Normandy6644]

If you're uncertain that 0.333... = 0.333..., why aren't you questioning whether 1 = 1? Or what about 1.000... = 1.000...? That sounds again like you're suggesting that "..." can have different "values", apart from just signifying that the sequence should continue. But does it really make sense to you that the same symbols should represent different things? Since we were the ones who defined what those symbols meant, why would we do that?
It's those ...'s that bother me. 8-[

Ok, off to class. I'm so tired right now. :-?

You want to spend time writing out all the 9's? :wink:

[Frog march]

0.999999999999999999999999999999999999999999999999 9999999999
99999999999999999999999999999999999999999999999999 9999999999
99999999999999999999999999999999999999999999999999 9999999999
99999999999999999999999999999999999999999999999999 9999999999
99999999999999999999999999999999999999999999999999 9999999999
99999999999999999999999999999999999999999999999999 9999999999
99999999999999999999999999999999999999999999999999 9999999999
999999999999999.............
hum..... you just have to hold down the '9' button a while.

[Grey]

Yep, it's 1. :)
Bases other than 10 were discussed extensively in the thread over at FWIS (http://loresinger.com/FWIS/viewtopic.php?p=21313#21313).
I fear, though, that while I think they were brought up to try to make the issue more clear, they just ended up confusing it further. :(

[Normandy6644]

hum..... you just have to hold down the '9' button a while.

Quite a long while to get them all. :D

[Grey]

It's those ...'s that bother me. 8-[
Right. So what about this one:

1.000... = 1.000...

True, not true, or sometimes true, as far as you're concerned?

[Frog march]

yes 1.000.....=1.000....

note the .000.... part of the number=zero to how ever many places you take them..

[Candy]

yes 1.000.....=1.000....

note the .000.... part of the number=zero to how ever many places you take them..
Then, I will say yes. Is this a trick question? 8-[

[Grey]

Then, I will say yes. Is this a trick question? 8-[
I'm really not trying to trick you, but I am trying to get a handle on exactly what your thought processes are (and in the process, perhaps you might find out more about your thoughts about this yourself), so that's why I'm asking a number of closely related questions, some of which may seem a little silly. :D

So, what's the difference between 1.000... = 1.000... and 0.333... = 0.333...? In the former case, the ellipsis just indicates a never-ending string of 0's, and it would indeed seem reasonable to assume that one such string is equal in value to another such string. In the latter case, the ellipsis indicates a never ending string of 3's. Why would it be possible for two neverending strings of 3's to have a different value from each other if it's not possible for two neverending strings of 0's to have different values?

[worzel]

Yep, it's 1. :)
Bases other than 10 were discussed extensively in the thread over at FWIS (http://loresinger.com/FWIS/viewtopic.php?p=21313#21313).
I fear, though, that while I think they were brought up to try to make the issue more clear, they just ended up confusing it further. :(
Guilty :oops:

I do think, though, that this tack may help for some people. I remember having one of those "a ha!" moments when I first discovered that any rational number has a finite expansion in some bases and a finitely representable expansion in any (rational) base.

[Candy]

So, what's the difference between 1.000... = 1.000... and 0.333... = 0.333...? In the former case, the ellipsis just indicates a never-ending string of 0's, and it would indeed seem reasonable to assume that one such string is equal in value to another such string. In the latter case, the ellipsis indicates a never ending string of 3's. Why would it be possible for two neverending strings of 3's to have a different value from each other if it's not possible for two neverending strings of 0's to have different values?
I see 1.000... as having a whole value. I see 0.333... as having an odd value.

To me, just because we've given 0.333... a value that we can visualize, 1/3, doesn't mean the values we visualize, 1/3 + 1/3 + 1/3, truly equal 1.

We are simplifying it (rounding ~off each individual odd value), so that we can understand and use it for more practical purposes.

[Frog march]

the 0.33333333333...... representation of 1/3 IS only an approximation, because you just CANT, show all the 3s, but 1/3 IS a real number, it represents an OPERATION, the division of 1 into three equal values, and represents just one of these segments. 1/3 is not the decimal representation of any number, it is a FRACTION.
If you divide a number into any number of parts and then put those parts back together, mathematicaly, you will get the same number that you started with, therfore 1/3+1/3+1/3 DOES represent 1.

[Candy]

1/3+1/3+1/3 DOES represent 1.
I agree, it represents 1.

[Captain Kidd]

So, what's the difference between 1.000... = 1.000... and 0.333... = 0.333...? In the former case, the ellipsis just indicates a never-ending string of 0's, and it would indeed seem reasonable to assume that one such string is equal in value to another such string. In the latter case, the ellipsis indicates a never ending string of 3's. Why would it be possible for two neverending strings of 3's to have a different value from each other if it's not possible for two neverending strings of 0's to have different values?
I see 1.000... as having a whole value. I see 0.333... as having an odd value.

To me, just because we've given 0.333... a value that we can visualize, 1/3, doesn't mean the values we visualize, 1/3 + 1/3 + 1/3, truly equal 1.

We are simplifying it (rounding ~off each individual odd value), so that we can understand and use it for more practical purposes.
It depends upon how you define your values.
The common agreement, on this thread, is that ... = infinitly repeating values
Therefore there is no rounding of 0.333... to a finite number of 3's. And thus it is 1/3.

Now if you define "..." as some finite sequence other than infinitly repeating, then, no, it won't add up to one.

But that's throwing an orange into the apple basket.

[Severian]

I agree, it represents 1

All we are talking about is representations. When you write a number, you are really just writing a representation anyway right? What does 2 mean other than the commonly agreed representation for the natural number immediately succeeding 1?

[Frog march]

2=0.999999......+0.999999......!!!

[Candy]

2=0.999999......+0.999999......!!!
Sure if 0.999999...... represents 1. I don't like this representation, though. :lol:

[Candy]

http://www.clicksmilies.com/s0105/auto/car-smiley-003.gif + http://www.clicksmilies.com/s0105/auto/car-smiley-003.gif = 2

http://www.clicksmilies.com/s0105/auto/car-smiley-003.gif represents 0.999999......

and 0.999999...... represents 1 :wink:

If you say so, Candy... #-o #-o #-o #-o

[Candy]

If you say so, Candy... #-o #-o #-o #-o
I'm really not trying to trick you, but I am trying to get a handle on exactly what your thought processes are (and in the process, perhaps you might find out more about your thoughts about this yourself), so that's why I'm asking a number of closely related questions, some of which may seem a little silly. :D
Pete, I was answering Grey’s statement. He wanted to understand my way of thinking. 8)

The common agreement, on this thread, is that ... = infinity repeating values
Therefore there is no rounding of 0.333... to a finite number of 3's. And thus it is 1/3.

Pete, my name does not equal infinity repeating values. It's simply Candy. :D

If you say so, Candy... #-o #-o #-o #-o
I'm really not trying to trick you, but I am trying to get a handle on exactly what your thought processes are (and in the process, perhaps you might find out more about your thoughts about this yourself), so that's why I'm asking a number of closely related questions, some of which may seem a little silly. :D
Pete, I was answering Grey’s statement. He wanted to understand my way of thinking. 8)

The common agreement, on this thread, is that ... = infinity repeating values
Therefore there is no rounding of 0.333... to a finite number of 3's. And thus it is 1/3.

Pete, my name does not equal infinity repeating values. It's simply Candy. :D

Eh??? :lol: :lol: :lol:

[Frog march]

I don't think that CANDY is a mathematical symbol, is it? :-s

[Candy]

I don't think that CANDY is a mathematical symbol, is it? :-s
I've heard shapely, does that count as mathematical? :P

I don't think that CANDY is a mathematical symbol, is it? :-s
I've heard shapely, does that count as mathematical? :P

It might?? :wink:

[Frog march]

8-[

[Candy]

8-[
Did you mean this? You're so cute. :D

http://home.att.net/~candy.stair/candycane.jpg

[Frog march]

that's the one!

[Candy]

Can I just say, I'm so happy that you guys aren't treating me like a total woo woo for the way I think about math? I'm glad you are taking the time to get inside of my head. Thank you. :D

[Normandy6644]

Can I just say, I'm so happy that you guys aren't treating me like a total woo woo for the way I think about math? I'm glad you are taking the time to get inside of my head. Thank you. :D

It's because we know you aren't a woo woo, and that you're quite intelligent, but are having a hard time grasping a difficult matter. And that's what we're here for!

[Candy]

Can I just say, I'm so happy that you guys aren't treating me like a total woo woo for the way I think about math? I'm glad you are taking the time to get inside of my head. Thank you. :D

It's because we know you aren't a woo woo, and that you're quite intelligent, but are having a hard time grasping a difficult matter. And that's what we're here for! :-#

Actually, I think I'm helping you open your mind. But you can look at your way, too. I should've stuck with Math (circa 198X)! :D

[SciFi Chick]

Can I just say, I'm so happy that you guys aren't treating me like a total woo woo for the way I think about math? I'm glad you are taking the time to get inside of my head. Thank you. :D

It's because we know you aren't a woo woo, and that you're quite intelligent, but are having a hard time grasping a difficult matter. And that's what we're here for! :-#

Actually, I think I'm helping you open your mind. But you can look at your way, too. I should've stuck with Math (circa 198X)! :D

No one here is changing their mind about the correct answer. They don't need to have their minds open. What you're suggesting with redefining math symbols makes no more sense than if you decided you didn't think 'o' is always 'o'. Maybe sometimes it's 'z'.

[Candy]

No one here is changing their mind about the correct answer. They don't need to have their minds open. What you're suggesting with redefining math symbols makes no more sense than if you decided you didn't think 'o' is always 'o'. Maybe sometimes it's 'z'.
Okay.

[Candy]

No one here is changing their mind about the correct answer. They don't need to have their minds open. What you're suggesting with redefining math symbols makes no more sense than if you decided you didn't think 'o' is always 'o'. Maybe sometimes it's 'z'.
Okay.
Why does your percentage keep shrinking toward NO? 8-[

[SciFi Chick]

No one here is changing their mind about the correct answer. They don't need to have their minds open. What you're suggesting with redefining math symbols makes no more sense than if you decided you didn't think 'o' is always 'o'. Maybe sometimes it's 'z'.
Okay.
Why does you percentage keep shrinking toward NO? 8-[

I didn't say everyone agreed, but since no one - not one person - has signed on and said that you changed their mind, for you to assume that that people voting no are doing so because of your argument is quite an assumption to say the least.

[Candy]

I didn't say everyone agreed, but since no one - not one person - has signed on and said that you changed their mind, for you to assume that that people voting no are doing so because of your argument is quite an assumption to say the least.
Then I ask them to step forward. You don't have to, just because SciFi wants evidence. :roll:

JUST BE YOURSELF! Do what you want. :wink:

[SciFi Chick]

I didn't say everyone agreed, but since no one - not one person - has signed on and said that you changed their mind, for you to assume that that people voting no are doing so because of your argument is quite an assumption to say the least.
Then I ask them to step forward. You don't have to, just because SciFi wants evidence. :roll:

JUST BE YOURSELF! Do what you want. :wink:

Of course. Just be yourself. Believe any nonsense you want, and then get offended if someone calls you a woo woo. After all, it's a free country.

[Frog march]

I believe
http://mathcentral.uregina.ca/QQ/database/QQ.09.01/catherine1.html
offers a simple proof.
There is no argument against it.

[Candy]

Of course. Just be yourself. Believe any nonsense you want, and then get offended if someone calls you a woo woo. After all, it's a free country.
You got that right, wicca sister! :o

[SciFi Chick]

Of course. Just be yourself. Believe any nonsense you want, and then get offended if someone calls you a woo woo. After all, it's a free country.
You got that right, wicca sister! :o

:-s

[Frog march]

Wic·ca (wĭk'ə)
n.
A polytheistic Neo-Pagan nature religion inspired by various pre-Christian western European beliefs, whose central deity is a mother goddess and which includes the use of herbal magic and benign witchcraft.
A group or community of believers or followers of this religion.
[Old English wicca, necromancer

:-?

[Candy]

Of course. Just be yourself. Believe any nonsense you want, and then get offended if someone calls you a woo woo. After all, it's a free country.
You got that right, wicca sister! :o

:-s
Don't you study wiccan? Sorry, I don't know the phrase.

[SciFi Chick]

Of course. Just be yourself. Believe any nonsense you want, and then get offended if someone calls you a woo woo. After all, it's a free country.
You got that right, wicca sister! :o

:-s
Don't you study wiccan? Sorry, I don't know the phrase.

No. I do not. What my religious beliefs or lack thereof have to do with this has to do with the subject at hand escapes me. Are you saying your issues with the proof are religious in nature?

Or is it that you think if you assassinate my character that will somehow vindicate your wrongness?

[SciFi Chick]

Wic·ca (wĭk'ə)
n.
A polytheistic Neo-Pagan nature religion inspired by various pre-Christian western European beliefs, whose central deity is a mother goddess and which includes the use of herbal magic and benign witchcraft.
A group or community of believers or followers of this religion.
[Old English wicca, necromancer

:-?

I understood what Wicca was. I didn't understand why the label was being applied to me. 8)

[Candy]

Of course. Just be yourself. Believe any nonsense you want, and then get offended if someone calls you a woo woo. After all, it's a free country.
You got that right, wicca sister! :o

:-s
Don't you study wiccan? Sorry, I don't know the phrase.

No. I do not. What my religious beliefs or lack thereof have to do with this has to do with the subject at hand escapes me. Are you saying your issues with the proof are religious in nature?

Or is it that you think if you assassinate my character that will somehow vindicate your wrongness?

Wait a minute. I could have sworn you were a 'witch' from previous post on here or on FWIS. Are you not?

I like math, but I would also like to know you! 8-[

[SciFi Chick]

No. I am definitely not a witch. I have studied wiccan due to my like of hte television show Buffy the Vampire Slayer.

My own religious or spiritual beliefs have been up in the air since I left Christianity. I do find some resonance with Celtic lore and the idea of an Otherworld, but I'm definitely not a witch.

I do like Hermione though. :D

[Frog march]

I wish I hadn't looked up the word now... :-?

[Candy]

Oh dear, studying witchcraft is not a bad thing. It's a religion. Practice all you want. :o

[Candy]

No. I am definitely not a witch. I have studied wiccan due to my like of hte television show Buffy the Vampire Slayer.
I thought those were vampires. ANGEL Rules!

[Candy]

Grey? Can we continue the appropriate conversations?

Before someone gets mad at me?

[SciFi Chick]

Oh dear, studying witchcraft is not a bad thing. It's a religion. Practice all you want. :o

I didn't say it was a bad thing. It's just not my belief. Please quit implying that it is.

[SciFi Chick]

I wish I hadn't looked up the word now... :-?

Why?

[Frog march]

well i didn't mean to cause a ruckus... :-?

[SciFi Chick]

No. I am definitely not a witch. I have studied wiccan due to my like of hte television show Buffy the Vampire Slayer.
I thought those were vampires. ANGEL Rules!

That just goes to show you haven't watched it very much. :wink:

[SciFi Chick]

well i didn't mean to cause a ruckus... :-?

You didn't cause a ruckus. No worries. 8)

[Frog march]

Buffy DOES slay vampires but I gather that she lives near the portal to hell and has other "types" of creatures to deal with.

[Eroica]

Before someone gets mad at me?
I think it's a bit late for that. :D

[SciFi Chick]

Buffy DOES slay vampires but I gather that she lives near the portal to hell and has other "types" of creatures to deal with.

Willow is Wiccan. :D

[Grey]

I see 1.000... as having a whole value. I see 0.333... as having an odd value.
But shouldn't it always have the same value at least?

We are simplifying it (rounding ~off each individual odd value), so that we can understand and use it for more practical purposes.
This is pure theoretical math. It has no practical purpose! :D But seriously, we aren't talking about some approximation, or rounding off at some number of digits, however large. We're really talking about an infinite string of digits, that never ends.

On some of these threads, a few people have used notation like 0.333...4, suggesting an infinite string of 3's, with a 4 at the end. Do you think that kind of notation is meaningful?

[edit for spelling]

[Grey]

Grey? Can we continue the appropriate conversations?

Before someone gets mad at me?
Whoops, sorry, I was out. Just trying to catch up now!

This one reall has created a stir, hasn't it?? :D :D :D :D

I can see how you can have one apple or one banana - meaning, to me anyway, a kind of unity in the real world...I THINK I can see how mathematical modelling might lead to an approximation 0.999999 apples...

Now, I suppose, the mathematical abstraction 0.999999 might translate to unity in the real world. But, does the mathematical abstraction equal the real world???

#-o #-o #-o #-o #-o 8-[ 8-[ 8-[ 8-[ 8-[ #-o #-o #-o :o :D :D :oops:

[Frog march]

It's like having a box which is divided up into 10 compartments nine of which are filled with something, the tenth compartment its self is divided into 10 equal compartments 9 of which are, again filled with something, the tenth compartment of this smaller arrangement is again divided into 10 compartments and on and on and on.........
can the box be said to have no empty compartments?

[Grey]

Now, I suppose, the mathematical abstraction 0.999999 might translate to unity in the real world. But, does the mathematical abstraction equal the real world???
Two points. First, we're talking not about 0.999999, but about 0.999999..., and that ellipsis is crucial to the issue.

Second, we're actually discussing just the mathematical abstraction itself. We can talk later about whether it has any application to the real world or not. :D

It's like having a box which is divided up into 10 compartments nine of which are filled with something, the tenth compartment its self is divided into 10 equal compartments 9 of which are, again filled with something, the tenth compartment of this smaller arrangement is again divided into 10 compartments and on and on and on.........
can the box be said to have no empty compartments?
That's a pretty interesting way of looking at things. And I think the box can indeed be said not to have any empty compartments. Pick any compartment at any level. It might be one of the nine filled ones at that level, in which case it's trivially not empty. If it's that tenth one, though, it's subdivided into ten compartments, nine of which are filled and the tenth one is further subdivided, so it's still not empty. There's no place where you'll find a compartment that's actually empty, since any compartment that's not just completely filled with something is subdivided.

[mickal555]

I have not voted yet
My maths teacher saids that they are not equil and all the peole in my class said I was an idiot for saying that...
I guess that settle's it..

[EvilBob]

I have not voted yet
My maths teacher saids that they are not equil and all the peole in my class said I was an idiot for saying that...
I guess that settle's it..

Actually, that's about the best reason for accepting that they ARE equal that I have read in these two whole threads.... :D

[SciFi Chick]

I have not voted yet
My maths teacher saids that they are not equil and all the peole in my class said I was an idiot for saying that...
I guess that settle's it..

Are you sure you presented it to your math teacher accurately?

[Grey]

Are you sure you presented it to your math teacher accurately?
I'm disappointed to hear that his math teacher said that. However, it also strikes me that, if his math teacher really believes they are not equal, he or she is perhaps also not likely to then acknowledge that a student knows more about the matter than he or she does.

[SciFi Chick]

Are you sure you presented it to your math teacher accurately?
I'm disappointed to hear that his math teacher said that. However, it also strikes me that, if his math teacher really believes they are not equal, he or she is perhaps also not likely to then acknowledge that a student knows more about the matter than he or she does.

I realize that, but we have been discussing this for months now, and people are still writing things like .9999999 without the ellipses. So, I was just trying to give him/her the benefit of the doubt, especially since mickal doesn't seem clear on it himself.

[Normandy6644]

Are you sure you presented it to your math teacher accurately?
I'm disappointed to hear that his math teacher said that. However, it also strikes me that, if his math teacher really believes they are not equal, he or she is perhaps also not likely to then acknowledge that a student knows more about the matter than he or she does.

I realize that, but we have been discussing this for months now, and people are still writing things like .9999999 without the ellipses. So, I was just trying to give him/her the benefit of the doubt, especially since mickal doesn't seem clear on it himself.

Yeah, I have to feel that a math teacher would know the correct answer (I know I remember discussing it in high school), but if it wasn't presented correctly that would affect the response.

[quote=Pete Tattum]

Second, we're actually discussing just the mathematical abstraction itself. We can talk later about whether it has any application to the real world or not. :D



Thank you Grey...then I admit I was wrong. :oops: 0.999999... must be equal to 1.0.

[Lurker]

It does have real world application, that's the point. The concept that an infinite series converges to a finite quantity is the basis for calculus. This is one of the basic tool used to understand the world around us. Try to develop Maxwell's equations with out it... try to analyze the forces in a modern structure with out it... try to understand gravitational force without it... try to develop the theory of relativity or quantum mechanics without it

The list goes on and on...

[Frog march]

0.999999...... is just the same as 1 minus 1/infinity and 1/infinity is generaly treated as being the same as ZERO.

[Grey]

0.999999...... is just the same as 1 minus 1/infinity and 1/infinity is generaly treated as being the same as ZERO.
See, I don't much like this way of stating it. Putting infinity in a formula like that makes it look like a number, and that makes it all too easy to think of it as a really big number, that's bigger than all the other numbers. So then it's all too easy to think "well, it's generally treated as being zero, but it's actually some really, really small number that we can treat as zero for most purposes". I thought your subdivided boxes were better. :D

[Frog march]

well I would use this
http://www.math.tifr.res.in/~shanta/pic/infinity.gif

but I haven't got it on my keyboard.
I know it isn't a number, it is a mathematical concept. 8-[

[mickal555]

Well I did say recuring, and useded some examples... but...

Later on though I went to Mr. bird the head of the maths department
"hi, Mr bird"
"greatings"
"um could I ask you somthing""
"shame....."
"Oh" *tucks in shirt*
Hey, you know 0.9999 recering and one, are they equil?
"Oh, yes if you have a piece of paper I'll show you why"
"It's OK I asked mr. walker and he said they wern't"
"No, they are...""
"OK thanks"

He's like super smart, kinda eccentric though... like he always knocks on doors before going through even if he is on the inside....
puts on his sunglasses inside...

Anyway yeah...

[Frog march]

maybe he's inspecting the doors for woodworm.. 8-[

[mickal555]

maybe he's inspecting the doors for woodworm.. 8-[
Glass

[Candy]

well I would use this
http://www.math.tifr.res.in/~shanta/pic/infinity.gif

but I haven't got it on my keyboard.
I know it isn't a number, it is a mathematical concept. 8-[
You can copy and paste it from word. [∞]

[mickal555]

I've voted

[Frog march]

to legalise gay marrage? to ban foxhunting???? =D>

[mickal555]

It depends on how you look at it I suppose....

[Disinfo Agent]

It does have real world application, that's the point. The concept that an infinite series converges to a finite quantity is the basis for calculus. This is one of the basic tool used to understand the world around us. Try to develop Maxwell's equations with out it... try to analyze the forces in a modern structure with out it... try to understand gravitational force without it... try to develop the theory of relativity or quantum mechanics without it

The list goes on and on...
For those who don't see (or have forgotten) the connection with infinite series:

0.99999.... = 0.9 + 0.09 + 0.009 + 0.0009 + ...

I must say it's curious how most people accept infinite sums without blinking, but some have a problem with infinite numerals.

0.999999...... is just the same as 1 minus 1/infinity and 1/infinity is generaly treated as being the same as ZERO.
I suppose that's how the "doubters" are reasoning, but, if you really think about it, why should 0.999999...... be as 1 minus 1/infinity? (Or even 1 - 1/(some infinitely large number)?)

Edited for clarity.

[Candy]

This is pure theoretical math. It has no practical purpose! :D But seriously, we aren't talking about some approximation, or rounding off at some number of digits, however large. We're really talking about an infinite string of digits, that never ends.
If it never ends, how could it possibly equal 1? To me, there has to be a "value or symbol or whatever" to assist in making 0.999... equal 1. If you are only making it equal 1, so that you can work with the number 1 easier, then you are misrepresenting the actual value.

On some of these threads, a few people have used notation like 0.333...4, suggesting an infinite string of 3's, with a 4 at the end. Do you think that kind of notation is meaningful?
For me, this would help with the addition part (if your meaning is to make one of the three 0.333... a 0.333...4). I still don't think that is the answer, though. Again, it would be misrepresenting the actual value of each 0.333...[end].

[azazul]

One of the nos should be a yes, I voted no and thought I had a good answer but it turns out I was mistaken when I tried to verify my answer.

[A Thousand Pardons]

For me, this would help with the addition part (if your meaning is to make one of the three 0.333... a 0.333...4). I still don't think that is the answer, though. Again, it would be misrepresenting the actual value of each 0.333...[end].
Exactly. :) You can't do that, without some major futchin around with the system. I know this isn't the lashing you expected, but I'll try:

Here's how Zeno figured it, 2300 years ago, with no modern math or strange symbols. Start off walking towards a point 1 km away, at 1 km per hour (taking your time with this). Of course, you're going to get there 1 hour from now. That's one way of looking at it. Another is you go half way, in half an hour. Then another quarter way in a quarter hour, another eiighth in an eighth of an hour, and so on. ( "..." in other words)

That's just another way of looking at it, you are not changing your speed. You still arrive at the end in one hour, even though you only go half way each time. You have to.

[Moose]

To me, there has to be a "value or symbol or whatever" to assist in making 0.999... equal 1.

There is. I've bolded it. If the elipsis didn't indicate an infinite repetition of 9s, then it wouldn't be equal to 1. It would then only be an approximation.

On some of these threads, a few people have used notation like 0.333...4, suggesting an infinite string of 3's, with a 4 at the end. Do you think that kind of notation is meaningful?

I'm not sure 0.333...4 is a valid (for lack of a better word) expression. "..." denotes an infinite repetition, not a break in a sequence. Infinity is infinite. Attempting to tack a terminating digit to an infinite sequence is somewhat similar to the schoolkid rebuttle: "Oh yeah? Infinity plus ONE." Doesn't exist.

Infinity isn't "the biggest number that exists". This implies an ending. Infinity doesn't end. There is no biggest number. Infinity is so big that the concepts of "biggest value" or "terminating digit" are both entirely meaningless and completely misleading.

[Candy]

I know this isn't the lashing you expected
Purrrrrrrrr! :D

That's just another way of looking at it, you are not changing your speed. You still arrive at the end in one hour, even though you only go half way each time. You have to.
Precisely, but we don't know exactly what helped the person to finally get to the end if he just keeps going half of his distance each time. You of all people have to know what I am thinking. 8-[

[Fram]

Attempting to tack a terminating digit to an infinite sequence is somewhat similar to the schoolkid rebuttle: "Oh yeah? Infinity plus ONE." Doesn't exist.

Infinity plus one does exist, but it is just infinity again. You can add, subtract, multiply, divide infinity by any number (not infinity) you want, and you will still get infinity (or minus infinity).

[A Thousand Pardons]

Precisely, but we don't know exactly what helped the person to finally get to the end if he just keeps going half of his distance each time.
Same thing that helped them get past the half way mark. After all, they had to go half way to that, then a quarter, then an eighth...

The resolution of the problem is exactly what we mean by smooth, uninterrupted motion. 9/10 + 9/100 + 9/1000 + ... equals 1.0 because we'd be in trouble if it didn't. It's why Zeno's paradox is not a paradox--although many fine people have pondered, and still ponder, the problem. I'm not one of those who think that it's indicative of educational decay. :)

You of all people have to know what I am thinking. 8-[
I've been there, just barely.

[Disinfo Agent]

Infinity plus one does exist, but it is just infinity again. You can add, subtract, multiply, divide infinity by any number (not infinity) you want (*), and you will still get infinity (or minus infinity).
(*) Except zero. :)

[Candy]

Precisely, but we don't know exactly what helped the person to finally get to the end if he just keeps going half of his distance each time.
Same thing that helped them get past the half way mark. After all, they had to go half way to that, then a quarter, then an eighth...
I wonder if introducing additional fractions is the reason the man will reach the end point. I was thinking a different way when you posed the initial question. I'm just throwing thoughts out, so don't beat me.

The resolution of the problem is exactly what we mean by smooth, uninterrupted motion. 9/10 + 9/100 + 9/1000 + ... equals 1.0 because we'd be in trouble if it didn't. It's why Zeno's paradox is not a paradox--although many fine people have pondered, and still ponder, the problem. I'm not one of those who think that it's indicative of educational decay. :)

I can compromise, and say that 0.999... "gives the illusion" of equally 1. Seeing it get so close by running almost parallel with 1 is a sure way to think it must eventually equal 1. :D

[Disinfo Agent]

I can compromise, and say that 0.999... "gives the illusion" of equally 1. Seeing it get so close by running almost parallel with 1 is a sure way to think it must eventually equal 1. :D
You are speaking of 0.999... as though it were a variable that took on several different values. Shouldn't it be a constant?

[Grey]

On some of these threads, a few people have used notation like 0.333...4, suggesting an infinite string of 3's, with a 4 at the end. Do you think that kind of notation is meaningful?
For me, this would help with the addition part (if your meaning is to make one of the three 0.333... a 0.333...4). I still don't think that is the answer, though. Again, it would be misrepresenting the actual value of each 0.333...[end].
To be fair, I don't consider this a meaningful notation, for the reasons Moose pointed out, and you might think about the implications. If having an infinite string of 3's with a 4 at the end makes sense to you, then you may still be thinking that there is an end to an infinite string of digits, when in fact, there's not.

Sadly, I fear that I'm going to be almost entirely occupied today, so I'll have to step back from the conversation until this evening. But I've been enjoying it, so I'll be back. Oh, and for what it's worth, when I was back in middle school I didn't buy this proof either, and I agree with A Thousand Pardons that it's actually a pretty intriguing question that clever people have been wrestling with for quite some time.

[Fram]

Infinity plus one does exist, but it is just infinity again. You can add, subtract, multiply, divide infinity by any number (not infinity) you want (*), and you will still get infinity (or minus infinity).
(*) Except zero. :)

:oops: Of course :oops:

[Candy]

On some of these threads, a few people have used notation like 0.333...4, suggesting an infinite string of 3's, with a 4 at the end. Do you think that kind of notation is meaningful?
For me, this would help with the addition part (if your meaning is to make one of the three 0.333... a 0.333...4). I still don't think that is the answer, though. Again, it would be misrepresenting the actual value of each 0.333...[end].
To be fair, I don't consider this a meaningful notation, for the reasons Moose pointed out, and you might think about the implications. If having an infinite string of 3's with a 4 at the end makes sense to you, then you may still be thinking that there is an end to an infinite string of digits, when in fact, there's not.
I didn't say I agreed with 0.333...4. :wink:

Sadly, I fear that I'm going to be almost entirely occupied today, so I'll have to step back from the conversation until this evening. But I've been enjoying it, so I'll be back. Oh, and for what it's worth, when I was back in middle school I didn't buy this proof either, and I agree with A Thousand Pardons that it's actually a pretty intriguing question that clever people have been wrestling with for quite some time. :D

[Disinfo Agent]

To be fair, I don't consider this a meaningful notation, for the reasons Moose pointed out, and you might think about the implications. If having an infinite string of 3's with a 4 at the end makes sense to you, then you may still be thinking that there is an end to an infinite string of digits, when in fact, there's not.
For the record, and since several posters have taken the conversation in that direction, I'm of the opinion that notations like "0.99...8"--zero followed by a point, followed by a countable infinity of nines, followed by an eight--could be made meaningful.
However, they are not sequences, in the ordinary sense of the word (http://pirate.shu.edu/projects/reals/numseq/sequence.html).

Edited for grammar.

[A Thousand Pardons]

doesn't mean the values we visualize, 1/3 + 1/3 + 1/3, truly equal 1.
1/3+1/3+1/3 DOES represent 1.
I agree, it represents 1.
Let me paraphrase, to make sure, here. Are you saying, that 1/3 + 1/3 + 1/3 might not equal 1?

[Candy]

I can compromise, and say that 0.999... "gives the illusion" of equally 1. Seeing it get so close by running almost parallel with 1 is a sure way to think it must eventually equal 1. :D
You are speaking of 0.999... as though it were a variable that took on several different values. Shouldn't it be a constant?
I was visualizing 0.999... and 1 on a diagram (not sure if this is the right term). To me, 0.999... moves each time we look at it with each additional 9 that gets tagged on the end of it. 8-[

[Disinfo Agent]

I was visualizing 0.999... and 1 on a diagram (not sure if this is the right term). To me, 0.999... moves each time we look at it with each additional 9 that gets tagged on the end of it. 8-[
What extra nines? Aren't they supposed to be all there already? :)

[Candy]

doesn't mean the values we visualize, 1/3 + 1/3 + 1/3, truly equal 1.
1/3+1/3+1/3 DOES represent 1.
I agree, it represents 1.
Let me paraphrase, to make sure, here. Are you saying, that 1/3 + 1/3 + 1/3 might not equal 1?
Yes.

[Frog march]

even if the chain of 3s did end, it wouldn't end in 4, that would be rounding off the wrong way, it would end in 3.

[A Thousand Pardons]

Let me paraphrase, to make sure, here. Are you saying, that 1/3 + 1/3 + 1/3 might not equal 1?
Yes.
And so 3/3 might not equal 1?

[Grey]

I was visualizing 0.999... and 1 on a diagram (not sure if this is the right term). To me, 0.999... moves each time we look at it with each additional 9 that gets tagged on the end of it. 8-[
Can't resist. Should be working. Must post again. :D

Rather than adding 9's over time, is there anyway that you can get yourself to imagine all of the 9's, all infinite count of them, all there at once, so that the value of 0.999... is in fact defined as something? Or do you feel that we have to truncate it at some point in order to give it a meaningful value?

[Candy]

I was visualizing 0.999... and 1 on a diagram (not sure if this is the right term). To me, 0.999... moves each time we look at it with each additional 9 that gets tagged on the end of it. 8-[
What extra nines? Aren't they supposed to be all there already? :)
I can't see it moving. I would assume it moves closer to 1 the bigger we imagine the number of 9's tagged on it. :-k

[Candy]

Let me paraphrase, to make sure, here. Are you saying, that 1/3 + 1/3 + 1/3 might not equal 1?
Yes.
And so 3/3 might not equal 1?
No.

[A Thousand Pardons]

Let me paraphrase, to make sure, here. Are you saying, that 1/3 + 1/3 + 1/3 might not equal 1?
Yes.
And so 3/3 might not equal 1?
No.
That seems to mean that 1/3 + 1/3 + 1/3 might not equal 3/3? Is that what you mean?

[Captain Kidd]

I was visualizing 0.999... and 1 on a diagram (not sure if this is the right term). To me, 0.999... moves each time we look at it with each additional 9 that gets tagged on the end of it. 8-[
What extra nines? Aren't they supposed to be all there already? :)
I can't see it moving. I would assume it moves closer to 1 the bigger we imagine the number of 9's tagged on it. :-k
If you're tagging on nines, then the number you're imagining contains finite nines. You can't add a nine to the end of an infinite number of nines because there is no end.

Your graph example, are you picturing an exponential curve?

[Moose]

What extra nines? Aren't they supposed to be all there already? :)

I can't see it moving. I would assume it moves closer to 1 the bigger we imagine the number of 9's tagged on it. :-k

Yes, exactly. As each approximation adds a nine to the series, you definitely do get closer to 1.

Goodness, Candy, you're so close... One more step and you're there. Here's the "punchline":

It's when there are an infinite number of nines, then it's exactly equal to one. We simply can't reach that point by any physical or iterative process. We can't write it out, and computers can't grind that number for us.

This is precisely what limit theory exists to solve.

[Candy]

Rather than adding 9's over time, is there anyway that you can get yourself to imagine all of the 9's, all infinite count of them, all there at once, so that the value of 0.999... is in fact defined as something? Or do you feel that we have to truncate it at some point in order to give it a meaningful value?

I can imagine it, but then it just runs parallel to 1. If 0.999... has an ending, then it wouldn't be infinite. It wouldn't be 1, either. :D

[Frog march]

Have you heard of fuzzy logic?
This is an electonic or programing technique where data is treated more flexibly than in ordinary systems and is used where a program might not be able to make a desision unless it was given some grey areas.
perhaps this is the approach you are taking? :-k

[Grey]

I can imagine it, but then it just runs parallel to 1.
I'm not quite sure what you mean by "runs parallel to".

If 0.999... has an ending, then it wouldn't be infinite. It wouldn't be 1, either. :D
This, I agree with entirely.

[Grey]

...unless it was given some grey areas.
Grey areas are good. :wink:

[Candy]

Let me paraphrase, to make sure, here. Are you saying, that 1/3 + 1/3 + 1/3 might not equal 1?
Yes.
And so 3/3 might not equal 1?
No.
That seems to mean that 1/3 + 1/3 + 1/3 might not equal 3/3? Is that what you mean?
I ok with 1/3 + 1/3 + 1/3 equally 3/3, therefore equally 1. It's how we got the value 1/3. Since 1/3 is 0.333..., we are forgeting about the infinity part. We are again fudging the value of 0.333... to give it a form we can work with for all practical purposes.

[Frog march]

fuzzy logic
n.
A form of algebra employing a range of values from “true” to “false” that is used in decision-making with imprecise data, as in artificial intelligence systems.

[Candy]

If you're tagging on nines, then the number you're imagining contains finite nines. You can't add a nine to the end of an infinite number of nines because there is no end.

Your graph example, are you picturing an exponential curve?
Is this wrong? I can see 1 never moving on a graph. I see 0.999... moving on a graph. Well, I can't really see it moving, but I am assuming it moves.

[A Thousand Pardons]

Let me paraphrase, to make sure, here. Are you saying, that 1/3 + 1/3 + 1/3 might not equal 1?
Yes.
And so 3/3 might not equal 1?
No.
That seems to mean that 1/3 + 1/3 + 1/3 might not equal 3/3? Is that what you mean?
I ok with 1/3 + 1/3 + 1/3 equally 3/3, therefore equally 1.

That's the part that seemed odd to me!

I'm glad we cleared that up. :)

[worzel]

It's why Zeno's paradox is not a paradox--although many fine people have pondered, and still ponder, the problem.
What problem?

[A Thousand Pardons]

It's why Zeno's paradox is not a paradox--although many fine people have pondered, and still ponder, the problem.
What problem?
Zeno's Paradox