Comments on: The well-ordering principle http://eli.thegreenplace.net/2009/07/09/the-well-ordering-principle/ Eli Bendersky's personal website Wed, 10 Mar 2010 17:32:25 +0000 http://wordpress.org/?v=2.9.2 hourly 1 By: Mark http://eli.thegreenplace.net/2009/07/09/the-well-ordering-principle/comment-page-1/#comment-182947 Mark Wed, 15 Jul 2009 08:36:23 +0000 http://eli.thegreenplace.net/?p=1772#comment-182947 You might consider why 'it is obvious' that W contains nonnegative integers. In fact, proving this when m is negative requires a second application of the well-ordering principle! You might consider why ‘it is obvious’ that W contains nonnegative integers. In fact, proving this when m is negative requires a second application of the well-ordering principle!

]]> By: ripper234 http://eli.thegreenplace.net/2009/07/09/the-well-ordering-principle/comment-page-1/#comment-181556 ripper234 Thu, 09 Jul 2009 16:49:10 +0000 http://eli.thegreenplace.net/?p=1772#comment-181556 For starters, read the entry on <a href="http://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox" rel="nofollow">Banach-Tarski Paradox</a>. For starters, read the entry on Banach-Tarski Paradox.

]]> By: eliben http://eli.thegreenplace.net/2009/07/09/the-well-ordering-principle/comment-page-1/#comment-181542 eliben Thu, 09 Jul 2009 15:09:41 +0000 http://eli.thegreenplace.net/?p=1772#comment-181542 Ron, to be completely honest, I don't think I have a good enough understanding of the philosophical foundations of mathematics to appreciate the "mind-boggling"-ness of this connection. Perhaps you can explain it to me some time. Ron, to be completely honest, I don’t think I have a good enough understanding of the philosophical foundations of mathematics to appreciate the “mind-boggling”-ness of this connection. Perhaps you can explain it to me some time.

]]> By: ripper234 http://eli.thegreenplace.net/2009/07/09/the-well-ordering-principle/comment-page-1/#comment-181511 ripper234 Thu, 09 Jul 2009 12:18:56 +0000 http://eli.thegreenplace.net/?p=1772#comment-181511 Have you read about the connection with the <a href="http://en.wikipedia.org/wiki/Axiom_of_choice" rel="nofollow">Axiom of Choice</a>? I find it mind-boggling. Have you read about the connection with the Axiom of Choice?

I find it mind-boggling.

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