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How can you easily prove that the set of real numbers is not countable? I don't think it's as easy as you claim, but I'm kind of a dummy so it's quite probably I'm wrong.

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Here's some background on the proof [1]. Here's a video explaining it little better [2].

[1] https://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument [2] https://www.youtube.com/watch?v=elvOZm0d4H0

I guess I was focusing on the word "easy", heh.

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.

Which school?

Carnegie Mellon

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.

Watch the video, its actually quite easy to follow.

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