Re: Ordinals

Newsgroups	sci.math
Date	2024-02-20 11:35 -0800
References	<Pine.NEB.4.64.1404190048420.27916@panix3.panix.com> <j4b4l91u1igos8jren2s8dlnoutnt8p8jj@4ax.com> <68b4l9l0to22jqn7skk9mdq9vcve4gpv9m@4ax.com>
Message-ID	<dd812ced-9275-4d52-9998-eccd0205515dn@googlegroups.com> (permalink)
Subject	Re: Ordinals
From	"markus...@gmail.com" <markusklyver@gmail.com>

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lördag 19 april 2014 kl. 10:11:25 UTC+2 skrev quasi:
> quasi wrote: 
> >William Elliot wrote: 
> >> 
> >>Does the set of all ordinals exist within ZF? 
> > 
> >It's too big to be a set.
> Hmmm ... 
> 
> It's certainly not a set in ZFC. 
> 
> I'm not sure if the "too big" criterion can be applied in ZF. 
> 
> But how would you _define_ such a set? 
> 
> Wouldn't the postulated existence of such a set fall victim to 
> Russell's paradox? 
> 
> quasi
No set can contain itself. The set of all ordinals would be a new ordinal, and thus contain itself. Ergo, there cannot be a set of all ordinals.

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Re: Ordinals "markus...@gmail.com" <markusklyver@gmail.com> - 2024-02-20 11:35 -0800
  Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-02-20 20:54 +0100
    Re: Ordinals "mitchr...@gmail.com" <mitchrae3323@gmail.com> - 2024-02-20 11:59 -0800
  Re: Ordinals Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-02-20 12:15 -0800
    Re: Ordinals Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-02-20 12:27 -0800
    Re: Ordinals Jim Burns <james.g.burns@att.net> - 2024-02-20 17:02 -0500
      Re: Ordinals Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-02-20 19:36 -0800
        Re: Ordinals Mild Shock <bursejan@gmail.com> - 2024-02-21 05:47 -0800
          Re: Ordinals Mild Shock <bursejan@gmail.com> - 2024-02-21 05:50 -0800
            Re: Ordinals Mild Shock <bursejan@gmail.com> - 2024-02-21 06:16 -0800
        Re: Ordinals Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-02-21 10:24 -0800
          Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-02-22 09:03 +0100
            Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-02-22 09:11 +0100
            Re: Ordinals Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-02-22 10:16 -0800
              Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-02-22 19:20 +0100
                Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-02-22 19:22 +0100
                Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-02-22 19:40 +0100
                Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-02-22 20:00 +0100
                Re: Ordinals Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-02-22 10:55 -0800
                Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-02-22 20:08 +0100
                Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-02-22 20:13 +0100
                Re: Ordinals Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-02-22 11:01 -0800
                Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-02-22 20:11 +0100
                Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-02-22 20:13 +0100
            Re: Ordinals Jim Burns <james.g.burns@att.net> - 2024-02-22 14:34 -0500
              Re: Ordinals Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-02-22 11:39 -0800
              Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-02-23 00:41 +0100
      Re: Ordinals WM <wolfgang.mueckenheim@tha.de> - 2024-02-21 08:33 +0000
        Re: Ordinals Jim Burns <james.g.burns@att.net> - 2024-02-21 12:59 -0500
          Re: Ordinals WM <wolfgang.mueckenheim@tha.de> - 2024-02-22 13:00 +0000
            Re: Ordinals Jim Burns <james.g.burns@att.net> - 2024-02-22 11:13 -0500
              Re: Ordinals WM <wolfgang.mueckenheim@tha.de> - 2024-02-23 08:47 +0000
                Semanticists candy (Was: Ordinals) Mild Shock <janburse@fastmail.fm> - 2024-02-26 12:58 +0100
                Re: Ordinals Jim Burns <james.g.burns@att.net> - 2024-02-27 14:25 -0500
                Re: Ordinals Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-02-27 11:59 -0800
                Re: Ordinals WM <wolfgang.mueckenheim@tha.de> - 2024-02-27 20:05 +0000
                Re: Ordinals Jim Burns <james.g.burns@att.net> - 2024-02-27 17:24 -0500
                Re: Ordinals WM <wolfgang.mueckenheim@tha.de> - 2024-02-28 09:48 +0000
                Re: Ordinals Jim Burns <james.g.burns@att.net> - 2024-02-28 06:52 -0500
                Re: Ordinals WM <wolfgang.mueckenheim@tha.de> - 2024-02-28 17:24 +0000
                Re: Ordinals Richard Damon <richard@damon-family.org> - 2024-02-28 17:07 -0500
                Re: Ordinals WM <wolfgang.mueckenheim@tha.de> - 2024-02-29 08:23 +0000
                Re: Ordinals Richard Damon <richard@damon-family.org> - 2024-02-29 07:35 -0500
                Re: Ordinals WM <wolfgang.mueckenheim@tha.de> - 2024-02-29 19:25 +0000
                Re: Ordinals "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-02-29 13:48 -0800
                Re: Ordinals Richard Damon <richard@damon-family.org> - 2024-02-29 22:12 -0500
                Re: Ordinals Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-02-29 19:36 -0800
                Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-03-01 20:38 +0100
                Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-03-01 20:52 +0100
                Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-03-01 21:08 +0100
                Re: Ordinals Jim Burns <james.g.burns@att.net> - 2024-03-01 15:56 -0500
                Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-03-01 22:53 +0100
                Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-03-01 23:11 +0100
                Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-03-01 23:33 +0100
                Re: Ordinals Jim Burns <james.g.burns@att.net> - 2024-03-01 19:41 -0500
                Re: Ordinals Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-03-01 20:15 -0800
                Re: Ordinals Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-03-02 10:49 -0800
                Re: Ordinals Mild Shock <janburse@fastmail.fm> - 2024-03-02 20:40 +0100
                Re: Ordinals Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-03-01 14:45 -0800
                Re: Ordinals WM <wolfgang.mueckenheim@tha.de> - 2024-03-01 08:47 +0000
                Re: Ordinals Richard Damon <richard@damon-family.org> - 2024-03-01 09:44 -0500
                Re: Ordinals WM <wolfgang.mueckenheim@tha.de> - 2024-03-01 18:29 +0000
                Re: Ordinals Richard Damon <richard@damon-family.org> - 2024-03-01 14:00 -0500
                Re: Ordinals WM <wolfgang.mueckenheim@tha.de> - 2024-03-02 12:36 +0000
                Re: Ordinals Richard Damon <richard@damon-family.org> - 2024-03-02 09:22 -0500
                Re: Ordinals WM <wolfgang.mueckenheim@tha.de> - 2024-03-02 15:25 +0000
  Re: Ordinals "mitchr...@gmail.com" <mitchrae3323@gmail.com> - 2024-02-20 17:21 -0800
    RSemanticists candy (Re: Ordinals) [Addendum] Mild Shock <janburse@fastmail.fm> - 2024-02-26 13:01 +0100

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