I wanted to post this in one of the other threads, but I couldn't decide which and I it didn't really fit in either. I know these have both been mentioned several times now (including a few by me!), but it can't hurt to look at them again, especially if you are new to the discussion. Here they are, in all their beauty.

*Note: If it seems excessive to start yet another thread about this, by all means delete it and I can post this in one of the others.

My math is very rusty, so I'm probably making a mistake here, but shouldn't that say 9/10^n in step 5 of the second one?

Yeah, there are a couple of mistakes in the second one. The sum should be 9*(1/10^n). Otherwise, your line 7 doesn't make any sense; 1-9/10 = 1/10

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Geometry is the science of correct reasoning on incorrect figures - George Pólya

Yep, fixed. Sorry, LaTeX can be screwy if you're in a hurry! ops:

Still not quite right.

You still have the 9/10 everywhere in line 7. You should have 9 \sum\limits_{n=1}^\infty \left ( \frac{1}{10} \right )^n = 9 \frac{\frac{1}{10}}{1-\frac{1}{10}}} = 1
or something

edit-heh I think you fixed it while I was typing this

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Geometry is the science of correct reasoning on incorrect figures - George Pólya

The way I look at it, we have an entire forum dedicated to the lunar conspiracies. Until this math issue is resolved, I don't care how many threads it takes.

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"The oxen are slow, but the earth is patient."

It still looks wrong to me. Look at step 7. You've got r=9/10 in the numerator and r=1/10 in the denominator.

r should be 1/10, shouldn't it? The sum is 9 times a geometric series with r=1/10.

That gives you 9*((1/10)/(1-(1/10)))

=9*((1/10)/(9/10))

=(9/10)/(9/10)

=1

Aaaaaghhh! I mentioned these threads to my wife.

Her: Well, it doesn't
Me: Yes it does
Her: No, it doesn't
Me: Yes it does
Her: No, it doesn't
Me: Yes it does
Her: No, it doesn't
Me: Yes it does
.
.
.

You get the picture.

So, now I'm really going to follow this simple solution once those kinks get worked out I'll show it to her.

His line 7 has 9/10 in the numerator...
Yours has 9*(1/10)
He just multiplied the 9 in

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Geometry is the science of correct reasoning on incorrect figures - George Pólya

OK, but in line 6 he still says that r=9/10. I guess that was confusing me.

Oh yeah, he sure does. He doesn't mean it

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Geometry is the science of correct reasoning on incorrect figures - George Pólya

I think you've just summed up the previous 3 threads on this subject! By the way, I haven't the math to follow the second method, but the first has completely clinched it for me. That's something I can show someone who doesn't agree....

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"Properly read, the Bible is the most potent force for atheism ever conceived." - Isaac Asimov

Argh!! I will fix this thing eventually!

We should add this to the file of "Who killed kennedy" and "How were the pyramids built". We're just never going to be able to solve it.

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Time cube is evil.

I'm not sure I agree about the "who killed Kennedy", but I'm with you 100% on the "how were the pyramids built"

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"The oxen are slow, but the earth is patient."

9*(1/10) is the same as 9/10..

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There, it should be okay now.

Note to self: Before posting something, make sure to doublecheck it! #-o

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Moraliser Overtax Porn

8-[ er..you still say r=9/10 between lines 5 and 6

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Geometry is the science of correct reasoning on incorrect figures - George Pólya

I suppose rule 6 is proven somewhere else, or is that common sense?

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Actually, he's fixed it; I see r=1/10 there. You might have to re-reload the page or something.

ah, my bad ops:

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Geometry is the science of correct reasoning on incorrect figures - George Pólya

RULE 6 ? 8-[

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It's not your fault. There is a tiny malicious gremlin who lives between .999... and 1 and perpetuates the myth that the two numbers are not equal by sneaking errors into proofs of their equality. It is necessary for him to do this because if everyone agreed that .999...=1, he would be left homeless.

can't be much of a home as it is.... 8-[

what with all the noise...

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Rule 6: There is NO ... rule six!
Rule 7: No poofters!

Bruce

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"For shame, gentlemen, pack your evidence a little better against another time."
-- John Dryden, "The Vindication of The Duke of Guise" 1684

I'm glad that's been cleared up... :-?

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Here you go: geometric series.

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"A witty saying proves nothing" Voltaire.
"All your bias are belong to us" Ara Pacis.

Is the first version (the simple one, the non-calculus one), correct?

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Don of Borg - Cool, Calm, Collective.

"Within the next generation I believe that the world's leaders will discover that infant conditioning and narco-hypnosis are more efficient, as instruments of government, than clubs and prisons, and that the lust for power can be just as completely satisfied by suggesting people into loving their servitude as by flogging them and kicking them into obedience." -- Aldous Huxley

In that first equation, how do we decide that n=.9999...

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"The oxen are slow, but the earth is patient."