[neutralino]

Originally Posted by Profpat But infinity never ends, you'll always have a .9 never ending.

Yes, that is what 0.999.. means. Think of it another way: the number 0.9999 is quite close to 1, but then the number 0.9999999999 is even closer, and 0.999999999999999999999999999 is even closer than that. Now consider the number 0.99... with infinitely many nines. This is the closest possible number to 1, but since we are dealing with real numbers I should be able to find another number closer to 1 still *. But, by definition I cannot, since there are infinitely many 9's. Thus 0.99.. must be equal to 1.

* There exists a real number between any two real numbers. To show this consider r<s. Then r<(r+s)/2<s.