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Re: Ordinals

From Jim Burns <james.g.burns@att.net>
Newsgroups sci.math
Subject Re: Ordinals
Date 2024-03-01 15:56 -0500
Organization A noiseless patient Spider
Message-ID <4097b7df-ccbf-401b-aec3-91a746c1a533@att.net> (permalink)
References (11 earlier) <urrh33$cbpp$7@i2pn2.org> <thicnWRrTbih0Hz4nZ2dnZfqn_udnZ2d@giganews.com> <urtarb$qese$1@solani.org> <urtblr$qfb8$1@solani.org> <urtckj$qfmv$1@solani.org>

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On 3/1/2024 3:08 PM, Mild Shock wrote:

> So I remember Jim Burns when he posited a more
> general approach, he said transfinite induction
> must be satisfied.

In a phrase I'm a little proud of, I said
transfinite.induction is well.order in drag.
One is a simple re-write of the other.

> Otherwise we can take this Quine atom x = {x},
> https://math.stackexchange.com/a/2874533
>
> And by a suitable interpretation of the circular
> h-trans definition, a definition that is not well-defined
> since it has no unique interpretation,
>
> we might judge this Quine atom an ordinal.
>
> LoL

Ah.
But an ordinal is
a _regular_ transitive set of transitive sets.
So, not x = {x}

A regular non.empty set A holds
a disjoint element B.
∃B ∈ A: A∩B = ∅

But, if A is transitive.transitive,
each element is a subset, and
∀B ∈ A: A∩B = B
Transitive.transitive A can only be regular
if one of its elements is 0

∅ ∈ A  ∧  ∅ ∈ A′ ties all the ordinals together.

It's a beautiful thing.

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Thread

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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