Infinity is bigger than you think - Numberphile
Infinity is bigger than you think - Numberphile on HackerTube: recommended by 3 Hacker News commenters across 4 separate months, 2014–2022.
Numberphile's James Grime explains Cantor's result that some infinities are bigger than others, including why the reals outnumber the integers. It is a short, accessible introduction to countable and uncountable infinity.
What HN commenters said
5 Hacker News comments link this video. Each one links back to its thread.
japhyrDec 2014Strongly recommends
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] - ▶ this video
in “Almost all numbers contain the digit “3” [video]” · View on HN
twelfthnightJul 2021Recommends
Here's some background on the proof [1]. Here's a video explaining it little better [2]. [1] [link] [2] ▶ this video
in “How many real numbers exist? New proof moves closer to an answer” · View on HN
cypharJun 2018Recommends
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: ▶ this video .
in “Are real numbers really real?” · View on HN
japhyrMar 2014Recommends
I like the numberphile series on youtube. I showed one in class where he explains how some infinities are bigger than others. My non-math-inclined students were able to follow it by watching several times, because they could see the entire process. They re-created the process themselves, rather than just trying to digest an explanation of an already-completed proof/ demonstration. Infinity is bigger than you think ▶ this video
in “LHC Physics Center bans Powerpoint, switches to whiteboard-only forums” · View on HN
AkronymusJul 2022Cites it
> There's no such thing as a bigger inifinite? Well, that is where the fun starts. Take every natural number, assign a unique real between 0 and 1 to it. Put all of them under each other. Now take the 1st digit of the first number, 2nd of the 2nd and so on, set it to a different digit than the one you took. Now you have a new, unique, real (Because it differs in at least one digit with every other real taken so far) but no more natural to assign it to. [link] ▶ this video
in “Absurd Trolley Problems” · View on HN