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How To Count Past Infinity

Support Vsauce, your brain, Alzheimer's research, and other YouTube educators by joining THE CURIOSITY BOX: a seasonal delivery of viral science toys made by Vsauce! A portion of all proceeds goes to Alzheimer's research and our Inquisitive Fellowship, a program that gives money and resources directly to growing science channels here on YouTube! https://www.curiositybox.com my twitter: @tweetsauce my instagram: electricpants Sources and links to learn more below! I’m very grateful to mathematician Hugh Woodin, Professor of Philosophy and Mathematics at Harvard, for taking the time on multiple occasions to discuss this topic with me and help me wrap my (finite) head around it. I’m also grateful to David Eisenbud, the Director of the Mathematical Sciences Research Institute (MSRI) and professor of mathematics at the University of California, Berkeley, for his help and for connecting me with Hugh Woodin. And of course, big thanks to Brady Haran who created the “mile of pi” seen in this video and connected me with all these mathematicians in the first place. His channel, Numberphile, is superb:    / numberphile   BOOKS related to these topics that I used: “The Outer Limits of Reason” by Noson S. Yanofsky: http://amzn.com/0262019353 “Infinity and The Mind” by Rudy Rucker: http://amzn.com/0691121273 “Roads to Infinity” by John C. Stilwell: http://amzn.com/1568814666 “More Precisely: The Math You Need to Do Philosophy” by Eric Steinhart: http://amzn.com/1551119099 “Satan, Cantor and Infinity: Mind-Boggling Puzzles” by Raymond M. Smullyan: http://amzn.com/0486470369 classic book that helps introduce concept of axioms: “Introduction to the Foundations of Mathematics” by Raymond L. Wilder: http://amzn.com/0486488209 Hugh Woodin speaking about infinity at the World Science Festival:    • Infinity: The Science of Endless   Names of large (finite) numbers: https://en.wikipedia.org/wiki/Names_o... Geoglyphs: The biggest number: https://goo.gl/maps/7GWcpnzo7iG2 Fovant badges: https://en.wikipedia.org/wiki/Fovant_... Battalion Park: https://en.wikipedia.org/wiki/Battali... A mile of pi [VIDEO]:    • Mile of Pi - Numberphile   Wikipedia’s great visualization of ordinals out to omega^omega: https://en.wikipedia.org/wiki/File:Om... as seen on: https://en.wikipedia.org/wiki/Ordinal... this is also a good page about ordinals: http://math.wikia.com/wiki/Ordinal_Nu... also: http://www.cut-the-knot.org/WhatIs/In... and: https://en.wikipedia.org/wiki/Order_type and https://en.wikipedia.org/wiki/Well-order Axioms: https://en.wikipedia.org/wiki/Axiom   / have_there_been_axioms_that_later_have_been   http://philosophy.stackexchange.com/q... http://www.cs.umd.edu/~gasarch/BLOGPA... http://www.cs.umd.edu/~gasarch/BLOGPA... THE UNREASONABLE EFFECTIVENSS OF MATHEMATICS IN THE NATURAL SCIENCES [PDF]: http://www.maths.ed.ac.uk/~aar/papers... https://en.wikipedia.org/wiki/The_Unr... Large Cardinal game based on 2048: http://cantorontheshore.blogspot.it/2... Other good resources: http://quibb.blogspot.com/2012/01/inf... http://plato.stanford.edu/entries/set... http://cantorsattic.info/Cantor%27s_A... http://cantorontheshore.blogspot.co.a... http://isomorphism.es/post/1078208142... https://lukepalmer.wordpress.com/2007... MUSIC BY:    / jakechudnow   http://www.audionetwork.com