I am trying to see how well people at BABB understand this, because other forums seem to show most people have a poor grasp of this idea.


There is a correct answer to the question. When I posted this in another forum, it was really surpised at how most people answered. So now I want to see how people here accept the correct answer. The correct answer is they are exactly equal. There is no difference between the two.

The way it was explained to me:

5/9=0.5555555555555......
6/9=0.66666666666..........
7/9=0.777777777777777....
8/9=0.88888888888..........
9/9=0.999999999999.......

5/5=1.000....
6/6=1.0000....
9/9=1.00000....

I voted no. I don't know why. 8-[

Also:

1/3 = 0.3333....
0.3333.... * 3 = 0.9999....
Therefore, 0.9999.... = 1

Irony is:

With Nine People, now having answered it, the Poll Numbers, ONLY EQUAL 99%!!!

8-[

__________________
If you Ignore YOUR Rights, they Will go away.

I'm going on what I was taught in Calculus. You must have two points to make a slope, so one point will be at x=1 and the other point will be the limit as x approaches 1, but never reaches it. Thus, assuming x approaches 1 from its lower side, x = 0.999999..., but does not equal 1.

Actually according to Calculus it is equal to 1. 0.99999... can be written as a limit. That limit converges onto 1. Thus 0.999999... equals 1.

Also the limit of x as a apporaches 1 is exactly equal to 1, not aproximatly 1.

From the numismatic world:
Fineness: the purity of a precious metal measured in 1,000 parts of an alloy: a gold bar of .995 fineness contains 995 parts gold and 5 parts of another metal. Example: the American Gold Eagle is .9167 fine, which means it is 91.67% gold. A Canadian Maple Leaf has a fineness of .999, meaning that it is 99.9% pure.

We are not talking about 0.999 but 0.9999999... a different number.

Oh.

Nope!

__________________
What's the youngest you could die of old age?

Yep

I would imagine that anyone who thinks differently has not yet encountered first semester calculus.

Or is an engineer. Frankly once you're over 0.51, to all intents and purposes you can round it to one. Why? Because it'll vanish into the measurement error when you actually build it....

Cheers
John

__________________
The engineer's mantra :-
The glass is neither half full or half empty, it's twice as big as it needs to be....

1 is an integer
0.9999999999~ is a real number.

they are not equal.

__________________
By asking questions we sometimes get the wrong answers, from wrong answers we learn to ask the right questions.

Integers are a subset of real numbers. 0.999999~is just a weird way to write 1.
If I ask if π = 3.14159..... you can also not say: No, π is a greek letter and 3.14159....... is a number, so they are not equal.

__________________
"Flying in space is risky business, but just staying on this planet is risky business too." - John Young, astronaut

ops:

Would anyone be equal to Candy?

Another way to think about it is to consider the difference between 1 and "0." followed by n 9s. The difference for finite n is given by 10^-n, so in the limit n->infinity, the difference between 1 and 0.9999... tends to zero, hence they are identical.

1 is used in binary (or any other base you care to name), and logic where 0.9999999~ is meaningless. Ok, maybe it's semantics but 0.999999~ is not equal and alike to 1 in all respects.

I do accept that the series (9*10^-1 +9*10-2 + ... + 9*10^-n + ...) >1 as n>infinity but this is only true (= 1) for base 10 calculations.

There is a wider world out there we should all be aware of.

__________________
By asking questions we sometimes get the wrong answers, from wrong answers we learn to ask the right questions.

Like when the ~Sumerians didn't have the number 0? 8-[

I don't think it is equal becuase it istn't. It is close though, and would be acceptable to round... espicially since you have infinate 9s.

Yes. If you don't agree, just ask yourself what you would get if you substracted 9.99999999999999........ from 1.

-9?

Exactly, which is the same thing as 1 subtract 10 therefore they are equal.

nice cover

That's exactly what I presume the Sumerians said. :-k

I hope with string theory, there is a whole other world opening up to us.

Back to math as we know it.
VVV

they are equal. A real number is defined as the limit of a sequence. If two sequences have the same limit, then both of them define the same number.

So there.

It's as close as you want and so there is no need to round to make it equal to 1.
But this here is a nice excercise on how diffcult it is to grasp the significance of what "limit" means. Am I correct when I say, if 0.9999~ would be not equal 1, then the whole calculus would fall into shreds?

Harald

__________________
"Flying in space is risky business, but just staying on this planet is risky business too." - John Young, astronaut

Close? Close?!?
You understand the concept of infinity, right?

__________________
"I'm making wheatloaf. It's like meatloaf, only with wheat"
"Isn't that just...bread?"

[strikeout]It depends.

Mathematically, they are quite different, but in the real world, the difference is so minor as to be irrelevant.[/strikeout]

In computing, the difference depends on whether your ALU rounds or truncates "infinite" floats.

[edit:] I think jfribrg just sold me. They are the same, mathematically, although the why is not an intuitive thing to grasp, I think.

Sure, for small enough values of 1.

:P :P :P :P :P :P

__________________
Starry, starry night...

My site TheSpacewriter.com
and my blog: TheSpaceWriter's Ramblings