# How To Count Past Infinity

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: https://www.youtube.com/user/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: https://youtu.be/KDCJZ81PwVM?t=29m45s

Names of large (finite) numbers: https://en.wikipedia.org/wiki/Names_of_large_numbers

Geoglyphs:

The biggest number: https://goo.gl/maps/7GWcpnzo7iG2

Fovant badges: https://en.wikipedia.org/wiki/Fovant_Badges

Battalion Park: https://en.wikipedia.org/wiki/Battalion_Park

A mile of pi [VIDEO]: https://www.youtube.com/watch?v=0r3cEKZiLmg

Wikipedia’s great visualization of ordinals out to omega^omega: https://en.wikipedia.org/wiki/File:Omega-exp-omega-labeled.svg

as seen on: https://en.wikipedia.org/wiki/Ordinal_number

this is also a good page about ordinals: http://math.wikia.com/wiki/Ordinal_Number

also: http://www.cut-the-knot.org/WhatIs/Infinity/Ordinals.shtml

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 proven false? from askscience

http://philosophy.stackexchange.com/questions/5922/what-is-the-difference-between-dogma-and-an-axiom

http://www.cs.umd.edu/~gasarch/BLOGPAPERS/belaxioms1.pdf

http://www.cs.umd.edu/~gasarch/BLOGPAPERS/belaxioms2.pdf

THE UNREASONABLE EFFECTIVENSS OF MATHEMATICS IN THE NATURAL SCIENCES

[PDF]: http://www.maths.ed.ac.uk/~aar/papers/wigner.pdf

https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences

Large Cardinal game based on 2048: http://cantorontheshore.blogspot.it/2014/10/one-reinhardt-and-counting.html

Other good resources:

http://quibb.blogspot.com/2012/01/infinity-first-transfinite-cardinal.html

http://plato.stanford.edu/entries/set-theory/

http://cantorsattic.info/Cantor%27s_Attic

http://cantorontheshore.blogspot.co.at/2014/09/artemis-fowl-and-large-cardinals_22.html

http://isomorphism.es/post/10782081422/what-comes-after-infinity-transfinite-arithmetic-and-ord

The Lesser of Infinitely Many Evils

MUSIC BY:

http://www.youtube.com/JakeChudnow

http://www.audionetwork.com

(9441234)

**Category:**Blog

**Tags:**after infinity, aleph, axiom, beyond, bigger than infinity, biggest infinity, biggest number, cantor, cardinals, College, Count, counting, end of numberline, exam, High School, hugh woodin, inaccessible, infinity, large cardinals, largest number, last number, learn, math, maths, michael stevens, number, omega, ordinal numbers, ordinals, Science, set theory, stem, test prep, the fault in our stars, theory, transfinite, types of number, vihart, Vsauce, woodin, woodin cardinal

Can you do a video about the Mandelbrot Set and mushrooms please????

Mandelbrot please

H E Y V S A U C E M I C H E A L H E R EIsnt the size of the uneverse ever expanding so in theory it is aleph-null

Hey I'm VSauce hi Micheal

who else stopped to count the number of dots?

no?

just me?

THIS EXPLAINS THE Yu-Gi-Oh! Infinite attack points

But what if I am to take a stack of money, count off bills until I have reached the dollar bill in the omega'th place, then burn the rest of the money, how rich am I? Putting a value to an omega.

the biggest number ive yet to count to is 1000000000000000000000000000000000

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Sorry for the long comment, i counted for 1000000000000000000000000000000000

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Years…

18:05

So what’s infinity with the exponent infinity and a infinite number of exponents x 1

Friend: On a scale of 1-10, how much do you want to kill yourself.

Me:

Shows them how to count past infinityMy brain hurts

omega looks like but cheeks

LIE!!!!!!!?????

the biggest number is 40 but thres 41 42 43 a sextilion

OMG I JUST LOOKED AT THE NAME HEY VSAUCE MICHEAL HERE

I. Have no idea what's going on…

Dank

:O

The answer is x + 1 = y