Quote:
Originally Posted by Illuminator
The proof saying that 1/3 is .333~ and therefore 3/3 is .999~ is completely hokey. You shouldn't even be allowed to perform or even assume direct operations on infinite expansions.
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Both 1/3 and 0.333~ are real numbers, and equal. Any operation you can perform on one can be performed on the other, as any real number can be operated upon. The results will be equal. There is no way that cannot be true.
If 0.333~ + 0.333~ can become 0.666~, then how can 0.666~ + 0.333~ not become 0.999~ but instead become 1? The other way around is equally absurd, because 2/3 + 1/3 = 1, and it is the same exact operation on the same exact numbers. Fact is, it becomes both, as both are the same.
This is how the real number system works. Deal with it.