Comments on: Game theory and the math of infinity http://mindyourdecisions.com/blog/2008/11/04/game-theory-and-the-math-of-infinity/ Articles on game theory and personal finance Sat, 20 Mar 2010 11:33:15 -0500 http://wordpress.org/?v=2.9.2 hourly 1 By: Presh Talwalkar http://mindyourdecisions.com/blog/2008/11/04/game-theory-and-the-math-of-infinity/comment-page-1/#comment-6094 Presh Talwalkar Wed, 23 Dec 2009 19:04:43 +0000 http://mindyourdecisions.com/blog/?p=807#comment-6094 <b><em>Chris</b></em>: You're right! Bob can definitely throw the game, just as one could lose in tic-tac-toe or in <a href="http://en.wikipedia.org/wiki/Hex_(board_game)" rel="nofollow">Hex</a> (a game with an unknown but provably winnable strategy for the first player). So whether Bob does win a particular game is irrelevant to the proof. And in fact, this game is not really practical to play--who has potentially infinite time to play a game? Chris: You’re right! Bob can definitely throw the game, just as one could lose in tic-tac-toe or in Hex (a game with an unknown but provably winnable strategy for the first player).

So whether Bob does win a particular game is irrelevant to the proof. And in fact, this game is not really practical to play–who has potentially infinite time to play a game?

]]> By: Chris http://mindyourdecisions.com/blog/2008/11/04/game-theory-and-the-math-of-infinity/comment-page-1/#comment-6088 Chris Tue, 22 Dec 2009 20:24:56 +0000 http://mindyourdecisions.com/blog/?p=807#comment-6088 Just because Bob CAN win, doesn't mean he WILL necessarily win. How would Bob know which subset Alice picked before the game started? Just because Bob CAN win, doesn’t mean he WILL necessarily win. How would Bob know which subset Alice picked before the game started?

]]> By: Presh Talwalkar http://mindyourdecisions.com/blog/2008/11/04/game-theory-and-the-math-of-infinity/comment-page-1/#comment-3439 Presh Talwalkar Fri, 07 Nov 2008 04:27:32 +0000 http://mindyourdecisions.com/blog/?p=807#comment-3439 <b><em>starwed</b></em>: Thanks for catching that and I've fixed it--it is a big error. I went back and see that I misread the paper. X is defined as the convergence of a_n. There is nothing that makes b_n converge to the same number as a_n. starwed:
Thanks for catching that and I’ve fixed it–it is a big error. I went back and see that I misread the paper. X is defined as the convergence of a_n. There is nothing that makes b_n converge to the same number as a_n.

]]> By: starwed http://mindyourdecisions.com/blog/2008/11/04/game-theory-and-the-math-of-infinity/comment-page-1/#comment-3420 starwed Thu, 06 Nov 2008 18:02:08 +0000 http://mindyourdecisions.com/blog/?p=807#comment-3420 X should just be the limit of a_n, I think, not both a and b. X should just be the limit of a_n, I think, not both a and b.

]]> By: Presh Talwalkar http://mindyourdecisions.com/blog/2008/11/04/game-theory-and-the-math-of-infinity/comment-page-1/#comment-3399 Presh Talwalkar Thu, 06 Nov 2008 06:06:37 +0000 http://mindyourdecisions.com/blog/?p=807#comment-3399 <b><em>Sarah</b></em>: Yes, I too was awestruck by the proof of uncountably infinite the first time I read it. It reminded me of the proof of why the square root of 2 is irrational in that it is both elegant and profound. Sarah:
Yes, I too was awestruck by the proof of uncountably infinite the first time I read it. It reminded me of the proof of why the square root of 2 is irrational in that it is both elegant and profound.

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