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#cantor'sdiagonalargument#infinity#settheory

Infinity is bigger than you think - Numberphile

Numberphile

4.7M subscribers • 28 videos on Hallway

YouTube
  • Recommended by 3 people: 3 on Hacker News.
  • A classic. People kept recommending it from 2014 to 2021.
  • Presented by James Grime, mathematician

Beginner. No background in the topic needed.

7.6M views14 years ago3 recommendations

Computer scienceComputation and complexity

James Grime explains Georg Cantor's proof that some infinities are larger than others, demonstrating why real numbers outnumber integers.

Sometimes infinity is even bigger than you think... Dr James Grime explains with a little help from Georg Cantor. More links & stuff in full description below ↓↓↓ Minute Physics video on this topic youtube.com/watch?v=A-QoutHCu4o (somewhat more fast-paced... but we did film ours BEFORE his was uploaded, so similarities are coincidental... well actually, no they are not... we are all building upon Cantor's work!!) NUMBERPHILE Website: numberphile.com/ Numberphile on Facebook: facebook.com/numberphile Numberphile tweets: twitter.com/numberphile Subscribe: bit.ly/Numberphile_Sub Videos by Brady Haran Patreon: patreon.com/numberphile Brady's videos subreddit: reddit.com/r/BradyHaran/ Brady's latest videos across all channels: bradyharanblog.com/ Sign up for (occasional) emails: eepurl.com/YdjL9 Numberphile T-Shirts: teespring.com/stores/numberphile Other merchandise: store.dftba.com/collections/numberphile

Why it's here

3 people recommend this

What people say. Recommended as an exceptionally clear and accessible introduction to Cantor's diagonal argument and the concept of uncountable infinity.

japhyron Hacker News • Recommends

On “Almost all numbers contain the digit “3” [video]”

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 - link to this video
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japhyron Hacker News • Recommends

On “LHC Physics Center bans Powerpoint, switches to whiteboard-only forums”

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 link to this video
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cypharon Hacker News • Recommends

On “Are real numbers really real?”

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: link to this video .
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twelfthnighton Hacker News • Recommends

On “How many real numbers exist? New proof moves closer to an answer”

Here's some background on the proof 1. Here's a video explaining it little better 2. 1 link 2 link to this video
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Akronymuson Hacker News • Mentions

On “Absurd Trolley Problems”

> 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 link to this video
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