Science
In reply to the discussion: If you're having math problems, I feel bad for you, son... [View all]napoleon_in_rags
(3,992 posts)If there's anything I've become more sure of since participating in this thread, its that fact. You could just as well say:
.999... = 1- (1/infinity), that latter term is also not equal to zero.
To see this, look at the number e defined as a limit:

http://en.wikipedia.org/wiki/E_(mathematical_constant)
And notice that if 1/infinity = zero, than e is equal to 1, which it isn't.
now what would a repeating decimal expansion of 1/infinity be? 0.00... repeating zeros forever, with a 1 on the "end" (which you never get to). subtract that from 1 and you get repeating 9's forever.
The meat of my argument is that a number can't be fully expressed in a number system where it requires infinite representation. The reason I chose those set numbers is because written in binary, a there is a 1 for each number in the set, a zero for each absent in the set. You can go on iterating them forever from the smallest to larger parts, so in this way they are like decimal representations that go on forever as well, just reversed so the decimals are more useful for talking about magnitude. In the big scheme of things, one doesn't make much more sense than the other. Infinite sets are just like infinitely long decimals or infinite integers. They really exist as objects with finite definitions, and that's where they belong, in the context where they can be finitely defined.