2017-09-21

[public] 146K views, 4.93K likes, 91.0 dislikes audio only

PBS Infinite Series

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Regular tic-tac-toe can get a bit boring -- if both players are playing optimally, it always ends in a draw. But what happens if you increase the width of the board? Or increase the dimension of the board? Or increase both?

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How the Axiom of Choice Gives Sizeless Sets | Infinite Series

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The standard game of tic-tac-toe is too easy. How can we, as mathematicians, play with the combinatorics of tic-tac-toe? There are (at least) three easy ways to modify the game of tic-tac-toe: increase the width of the board - like *this* 5x5 board - increase the dimension of the board - like *this* 3x3x3 board - or increase both, like this 4x4x4 board.

Challenge Winner of the How the Axiom of Choice Gives Sizeless Sets:

For Your Math

Written and Hosted by Kelsey Houston-Edwards

Produced by Rusty Ward

Graphics by Ray Lux

Assistant Editing and Sound Design by Mike Petrow

Made by Kornhaber Brown (www.kornhaberbrown.com)

Resources:

Hales/Jewett paper: http://www.ams.org/journals/tran/1963-106-02/S0002-9947-1963-0143712-1/S0002-9947-1963-0143712-1.pdf

Golomb/Hales paper: http://library.msri.org/books/Book42/files/golomb.pdf

https://www.youtube.com/watch?v=p1YzYLzRwtk

http://www.austms.org.au/Gazette/2005/Jul05/mathellaneous.pdf

Special Thanks: Benjamin Houston-Edwards and Nathan Kaplan

Mathologer Video:

/youtube/video/aDOP0XynAzA

Special thanks to Matthew O'Connor and Yana Chernobilsky who are supporting us on Patreon at the Identity level!

And thanks to Mauricio Pacheco and Nicholas Rose who are supporting us on Patreon at the Lemma level!