Game Moderator
Mod Boss
7846
May 29th 2014, 4:12:37
@brainwave: if that's true then you can't have a decimal representation of 1/3rd either..
0.33333333... is always less than 1/3 by your logic. However this contradicts several facets of number theory and real analysis. By definition, any repeating decimal with a pattern can be expressed as a rational number A/B where A and B are integers (they can be the same integer, B cannot be 0 :P)
So X = 0.33333....
10X = 3.333333333...
this 9X = 3
and X = 3/9 = 1/3.
Now lets try that with 0.999999....
X = 0.9999....
10X = 9.999999999....
9X = 9
X = 1.
See?
You can't tell me that my logic works for all repeating decimals except for 9... the way I'm doing multiplication and subtraction is well defined for *all* real numbers, and division (the way I'm doing it) for all real numbers except 0:P
Even if you don't agree with me, 0.9999999.... must be expressible as A/B. So if it isn't 1, what is it?
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