Infinity is bigger than you think - Numberphile

What people said

japhyr · 2014-12 · Strong recommendation

I teach high school math and science. I had a group of students do a mini-project around the question, "Is there anything bigger than infinity?" The core of the project was students watching this numberphile video [0], and recreating his reasoning on their own. That project helped them reason about higher-level math in a way they never thought themselves capable. The idea of "magic" never came up, but they certainly spoke about their sense of wonder at higher-level math. I really appreciate the way he presents mathematical concepts. [0] - [VIDEO]

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twelfthnight · 2021-07 · Recommendation

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

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cyphar · 2018-06 · Recommendation

Yes, because if there were such a list then you could assign a 1-to-1 mapping (by list index) of each number between 0 and 1 to a whole number which would prove they have the same size. If it is impossible to have a complete list of all real numbers between 0 and 1 then there cannot be such a mapping, and thus you'll "run out" of integers before you've counted all of the reals (more correctly you're showing that the size must be larger because if it was smaller or of equal size it could fit in such a list). Numberphile did a pretty good introductory video to this if you want to learn more: [VIDEO] .

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