So ... One ISN'T the loneliest number? =o/

The rationale escapes me. How does he figure that he would ever reach the end of integers?

More to the point, the number infinity isn't a real number, so the fact that you can double infinity and still have infinity doesn't mean your second infinity is somehow "bigger" than your first infinity, even if you have infinity times infinity to the power of infinity.

I wonder what Vi Hart would have to say about this. I'm pretty sure I've heard her say that infinity is not, in fact, a number at all, so quantifying and comparing it doesn't make sense.

Anybody?

He's using Cantor's diagonal argument, but not explaining it very well. Read the article (because I won't be able to explain it any better). The set of all integers is countably infinite, and the set of all real numbers is uncountably infinite (has a larger cardinality larger than the natural numbers).