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Taedrin
Gallente
Golden Mechanization Protectorate
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Posted - 2009.05.08 04:21:00 -
[1]
Edited by: Taedrin on 08/05/2009 04:21:55
Edited by: Taedrin on 08/05/2009 04:21:35
That proof actually makes no sense to me, as you are performing arithmetic with infinity (a number which extends into infinity, to be specific). What you REALLY want to say is this:
x
lim x->inf ∑ 9/(10^x) = 1
1
Here the concept of infinity is restricted to end behavior analysis, and you don't have to do any arithmetic with it.
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Taedrin
Gallente
Golden Mechanization Protectorate
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Posted - 2009.05.08 21:09:00 -
[2]
 Originally by: Kazuo Ishiguro
At the 10n - n step, he has to make the assumption that the 0.999... part of 9.99... is convergent. Therefore it doesn't constitute proof of convergence.
Which is why you convert the number into an infinite series and then do end behavior analysis to determine the value that it converges too 
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Taedrin
Gallente
Golden Mechanization Protectorate
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Posted - 2009.05.09 03:44:00 -
[3]
Originally by: FOl2TY8
Originally by: Taedrin
x
lim x->inf ∑ 9/(10^x) = 1
1
I have no idea what this means. I do however know how to be mean to a chick and still get laid.
It means
9/10 + 9/100 + 9/1,000 + 9/10,000 + 9/100,000 and then take the limit of this pattern as you continue to infinity. You will notice that 9/10 + 9/100 + 9/1,000 + ... is similar to .99999999..., if not exactly the same.
Essentially, it is the mathematically correct way to say that for every 9 that you add to the end of .9999999999..., you get a little bit closer to 1. If you take this to infinity, the asymptote is 1.
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Taedrin
Gallente
Golden Mechanization Protectorate
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Posted - 2009.05.12 15:21:00 -
[4]
Originally by: Gara Al'Malik
Another proof that 0.999... = 1.
Suppose that 0.999... < 1.
Now there exists e > 0 such that 0.999... + e = 1.
Let's write e in the decimal form e_1,e_2e_3e_4...
Since e > 0, e_i > 0 for some i. However in decimal place i, 0.999... has 9 and so the sum 0.999... + e > 1, which is a contradiction.
So now we know that 0.999... >= 1.
Similarly we can rule out 0.999... > 1.
The only possibility is then that 0.999... = 1
OOOOOO - nice proof.
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