Quote Originally Posted by omnitarian
But you never reach the end of the line, because there are an infinite number of zeroes. Just like there is no final 9 in .999... there is no 1 in .000...1.

So, depending on what logic you use, you could say that .000...1 = 0, or that .000...1 = .000...1, or that .000...1 is illogical.
in·fi·nite - adj.
1. Having no boundaries or limits.
bound·a·ry n.
1. Something that indicates a border or limit.

If there's a 1 at the end it has a boundary and a limit as it can't proceed beyond the 1.

Quote Originally Posted by Arche
Actually, you'll find that you can get infinites of different "sizes", as it were, so it's not quite boolean The infinity you get from counting all rational numbers is a smaller infinity than the infinity gotton from counting all irrational numbers, as one example. This'll require me to go back to my notes from 2 years ago on how to prove this one though [/j]
Yeah, I'm curious to see that proof. I thought that all infinites are equal.