Re: The Banach-Tarski Paradox

From	Fabian Russell <root@localhost.localdomain>
Newsgroups	sci.physics
Subject	Re: The Banach-Tarski Paradox
Date	2015-11-07 20:59 +0000
Organization	NewsGuy - Unlimited Usenet $23.95
Message-ID	<pan.2015.11.07.20.59.52@localhost.localdomain> (permalink)
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On Sat, 07 Nov 2015 14:40:22 -0600, Sam Wormley wrote:

>> It is about making two from one, with
> 
>    Not too shabby
>

Sorry, Wormley.  It's not about that at all.

The BT-Paradox is all about the Axiom of Choice and nothing else.

In typical fashion, brain-dead Wormley picks isolated and dazzling
topics from the YouTube archives without understanding the big
picture.

Would you care to tell us about some more mathematical pathologies
that can be attributed to the Axiom of Choice?














>  > https://en.wikipedia.org/wiki/Banach–Tarski_paradox
> 
>  > The Banach–Tarski paradox is a theorem in set-theoretic geometry,
>  > which states the following: Given a solid ball in 3‑dimensional
>  > space, there exists a decomposition of the ball into a finite number
>  > of disjoint subsets, which can then be put back together in a
>  > different way to yield two identical copies of the original ball.
>  > Indeed, the reassembly process involves only moving the pieces around
>  > and rotating them, without changing their shape. However, the pieces
>  > themselves are not "solids" in the usual sense, but infinite
>  > scatterings of points. The reconstruction can work with as few as
>  > five pieces.[1]
>  >
>  > A stronger form of the theorem implies that given any two
>  > "reasonable" solid objects (such as a small ball and a huge ball),
>  > either one can be reassembled into the other. This is often stated
>  > informally as "a pea can be chopped up and reassembled into the Sun"
>  > and called the "pea and the Sun paradox".

Thread

The Banach–Tarski Paradox Sam Wormley <swormley1@gmail.com> - 2015-11-07 09:10 -0600
  Re: The Banach–Tarski Paradox Edgardo Alcantara <edgardoalcantara@carosseryrepair.org> - 2015-11-07 15:17 +0000
  Re: The Banach-Tarski Paradox "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2015-11-07 09:51 -0800
    Re: The Banach-Tarski Paradox Sam Wormley <swormley1@gmail.com> - 2015-11-07 12:20 -0600
      Re: The Banach-Tarski Paradox "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2015-11-07 10:36 -0800
        Re: The Banach-Tarski Paradox "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2015-11-07 10:46 -0800
          Re: The Banach-Tarski Paradox "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2015-11-07 11:41 -0800
        Re: The Banach-Tarski Paradox Sam Wormley <swormley1@gmail.com> - 2015-11-07 14:04 -0600
          Re: The Banach-Tarski Paradox "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2015-11-07 12:27 -0800
            Re: The Banach-Tarski Paradox Sam Wormley <swormley1@gmail.com> - 2015-11-07 14:40 -0600
              Re: The Banach-Tarski Paradox Fabian Russell <root@localhost.localdomain> - 2015-11-07 20:59 +0000
              Re: The Banach-Tarski Paradox noTthaTguY <abu.kuanysh05@gmail.com> - 2015-11-08 08:51 -0800
            Re: The Banach-Tarski Paradox "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2015-11-07 14:25 -0800
              Re: The Banach-Tarski Paradox "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2015-11-07 18:59 -0800
                Re: The Banach-Tarski Paradox "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2015-11-09 07:59 -0800
          Re: The Banach-Tarski Paradox jimp@specsol.spam.sux.com - 2015-11-07 20:23 +0000
  Re: The Banach–Tarski Paradox Fabian Russell <root@localhost.localdomain> - 2015-11-07 19:18 +0000
    Re: The Banach–Tarski Paradox Odd Bodkin <bodkinodd@gmail.com> - 2015-11-09 08:38 -0600
      Re: The Banach–Tarski Paradox Fabian Russell <root@localhost.localdomain> - 2015-11-09 17:53 +0000
        Re: The Banach–Tarski Paradox Odd Bodkin <bodkinodd@gmail.com> - 2015-11-09 11:58 -0600
          Re: The Banach–Tarski Paradox Fabian Russell <root@localhost.localdomain> - 2015-11-09 18:55 +0000
            Re: The Banach–Tarski Paradox Odd Bodkin <bodkinodd@gmail.com> - 2015-11-09 17:10 -0600
              Re: The Banach–Tarski Paradox Fabian Russell <root@localhost.localdomain> - 2015-11-10 00:13 +0000
                Re: The Banach-Tarski Paradox "Ross A. Finlayson" <ross.finlayson@gmail.com> - 2015-11-09 17:12 -0800
                Re: The Banach–Tarski Paradox Odd Bodkin <bodkinodd@gmail.com> - 2015-11-10 08:35 -0600
                Re: The Banach–Tarski Paradox Fabian Russell <root@localhost.localdomain> - 2015-11-10 15:08 +0000
                Re: The Banach–Tarski Paradox Odd Bodkin <bodkinodd@gmail.com> - 2015-11-10 13:50 -0600
                Re: The Banach–Tarski Paradox Fabian Russell <root@localhost.localdomain> - 2015-11-10 23:47 +0000
                Re: The Banach–Tarski Paradox Odd Bodkin <bodkinodd@gmail.com> - 2015-11-10 19:40 -0600
                Re: The Banach–Tarski Paradox Fabian Russell <root@localhost.localdomain> - 2015-11-11 02:32 +0000
                Re: The Banach–Tarski Paradox Odd Bodkin <bodkinodd@gmail.com> - 2015-11-10 20:49 -0600

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