You do this in sophomore level Real Analysis. So as far as pure math goes, easy.
> sophomore level Real Analysis
Hmm?
We did this first semester freshman year at my school in a single lecture in a 100 level "concepts of mathematics" course. I get that there's a certain amount of "it's hard to wrap your head around infinity" but really this proof is pretty well trodden by students not far into learning mathematics.
I was homeschooled, so I was shown this in middle school hah. I think math camps and the like also tend to teach it before college.
Which school?
Carnegie Mellon
Watch the video, its actually quite easy to follow.