I know, stupid question. But humor me for a sec. First off, we know that all real numbers have two numbers which are infinitely close to them, right? That would seem to be, for any given value of x,
x ± y
y = .000...1
But here's the thing:
y + .999... = 1
And, of course, we all know that .999... = 1, so that means that y = 0, right? Which means that all numbers infinitely close to one another, which represents the entirety of the real number line, are equal, right? Something here is screwed up, but for the life of me I can't figure out what.
PS, I wasn't sure what tag to give this, so feel free to edit them.