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Re: Contradiction of bijections as a measure for infinite sets

From Dieter Heidorn <d.heidorn@t-online.de>
Newsgroups sci.math
Subject Re: Contradiction of bijections as a measure for infinite sets
Date 2024-03-24 22:02 +0100
Message-ID <l6binqF7ljpU1@mid.individual.net> (permalink)
References <qHqKnNhkFFpow5Tl3Eiz12-8JEI@jntp> <VYLp-BjAIbWT-h39YGH1pWjyXGI@jntp>

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WM schrieb:
> 
> Does ℕ = {1, 2, 3, ...} contain all natural numbers such that none
> can be added?
> 

Sure - adding a number that is already contained in ℕ, doesn't change
the cardinality of the set, since equal elements are counted as one
element.

But you can do the following described by Cantor:

    "That ℵo is a transfinite number, that is to say, is
     not equal to any finite number μ, follows from the
     simple fact that, if to the aggregate {ν} is added a
     new element e_0, the union-aggregate ({ν}, e_0 ) is
     equivalent to the original aggregate {ν}. For we
     can think of this reciprocally univocal correspondence
     between them: to the element e_0 of the first
     corresponds the element 1 of the second, and to the
     element ν of the first corresponds the element ν + 1 of
     the other. By §3 we thus have

        (2)      ℵo + 1 = ℵo "

(Georg Cantor:
  Contributions to the founding of the theory of tranfinite numbers.
  Dover Publications, 1915; p.104)

> If so, then the bijection of ℕ with E = {2, 4, 6, ...} would prove
> that both sets have the same number of elements.

Infinite sets don't have a "number of elements". This concept (which can
only be used for finite sets) is generalized for infinite sets by the
concept of "transfinite cardinal numbers".

And indeed: there is a bijection from the set of natural numbers ℕ
to the set of even natural numbers 𝔼 = {2, 4, 6, ..}.

    f: ℕ → 𝔼 ,  n ↦ 2n

This function is both injective (or one-to-one) and surjective (or
onto), thus it is bijective.

> Then the completion of E resulting in E = {1, 2, 3, 4, 5, 6, ...}
> would double the number of its elements. Then there are more natural
> numbers than were originally in ℕ.

Rubbish. The cardinality of an infinite set is described by an
transfinite cardinal number and not by a finite "number of elements".
Your problem is: You try to apply facts, that hold for finite sets,
on infinite sets. That doesn't work.

Dieter Heidorn

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V WM <wolfgang.mueckenheim@tha.de> - 2024-03-24 20:00 +0000
  Re: V "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-24 13:11 -0700
    Re: V WM <wolfgang.mueckenheim@tha.de> - 2024-03-24 20:13 +0000
      Re: V "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-24 13:16 -0700
        Re: V WM <wolfgang.mueckenheim@tha.de> - 2024-03-24 20:20 +0000
          Re: V "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-24 14:33 -0700
            Re: V WM <wolfgang.mueckenheim@tha.de> - 2024-03-25 11:23 +0000
              Re: V "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-25 20:40 -0700
                Re: V WM <wolfgang.mueckenheim@tha.de> - 2024-03-26 13:11 +0000
                Re: V "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-26 12:56 -0700
                Re: V WM <wolfgang.mueckenheim@tha.de> - 2024-03-27 13:50 +0000
                Re: V "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-27 13:49 -0700
                Re: V WM <wolfgang.mueckenheim@tha.de> - 2024-03-28 19:53 +0000
                Re: V "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-28 13:31 -0700
                Re: V "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-28 13:34 -0700
                Re: V "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-26 13:00 -0700
                Re: V "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-26 13:19 -0700
                Re: V "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-26 13:29 -0700
          Re: V "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-24 14:37 -0700
  Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-24 20:11 +0000
    Re: Contradiction of bijections as a measure for infinite sets Dieter Heidorn <d.heidorn@t-online.de> - 2024-03-24 22:02 +0100
      Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-25 11:10 +0000
        Re: Contradiction of bijections as a measure for infinite sets Richard Damon <richard@damon-family.org> - 2024-03-25 07:25 -0400
          Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-25 21:45 +0000
        Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-03-25 15:38 -0400
          Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-25 22:01 +0000
          Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-25 22:11 +0000
            Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-03-25 20:04 -0400
              Re: Contradiction of bijections as a measure for infinite sets "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-25 21:43 -0700
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-03-26 11:40 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-27 13:38 +0000
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-03-27 14:54 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-28 20:07 +0000
                Re: Contradiction of bijections as a measure for infinite sets "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-28 13:33 -0700
                Re: Contradiction of bijections as a measure for infinite sets Richard Damon <richard@damon-family.org> - 2024-03-29 09:29 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-30 16:01 +0000
                Re: Contradiction of bijections as a measure for infinite sets Richard Damon <richard@damon-family.org> - 2024-03-30 13:47 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-31 12:15 +0000
                Re: Contradiction of bijections as a measure for infinite sets Richard Damon <richard@damon-family.org> - 2024-03-31 14:18 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-01 15:37 +0000
                Re: Contradiction of bijections as a measure for infinite sets FromTheRafters <FTR@nomail.afraid.org> - 2024-04-01 13:30 -0400
                Re: Contradiction of bijections as a measure for infinite sets Richard Damon <richard@damon-family.org> - 2024-04-01 19:03 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-02 07:36 +0000
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-04-02 13:51 -0400
                Re: Contradiction of bijections as a measure for infinite sets Moebius <moebius@example.invalid> - 2024-04-02 22:52 +0200
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-04-02 17:40 -0400
                Re: Contradiction of bijections as a measure for infinite sets Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-04-02 15:06 -0700
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-04-02 19:25 -0400
                Re: Contradiction of bijections as a measure for infinite sets Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-04-02 20:52 -0700
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-04-03 09:13 -0400
                Re: Contradiction of bijections as a measure for infinite sets Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-04-03 19:13 -0700
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-04-04 15:01 -0400
                Re: Contradiction of bijections as a measure for infinite sets Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-04-04 20:28 -0700
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-04-05 14:04 -0400
                Re: Contradiction of bijections as a measure for infinite sets Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-04-05 19:37 -0700
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-04-06 09:31 -0400
                Re: Contradiction of bijections as a measure for infinite sets Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-04-06 08:42 -0700
                Re: Contradiction of bijections as a measure for infinite sets Moebius <moebius@example.invalid> - 2024-04-03 01:14 +0200
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-03 13:32 +0000
                Re: Contradiction of bijections as a measure for infinite sets FromTheRafters <FTR@nomail.afraid.org> - 2024-04-03 11:59 -0400
                Re: Contradiction of bijections as a measure for infinite sets Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-04-03 19:43 -0700
                Re: Contradiction of bijections as a measure for infinite sets Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-04-03 20:06 -0700
                Re: Contradiction of bijections as a measure for infinite sets FromTheRafters <FTR@nomail.afraid.org> - 2024-04-05 08:48 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-04 09:33 +0000
                Re: Contradiction of bijections as a measure for infinite sets Richard Damon <richard@damon-family.org> - 2024-04-04 08:19 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-04 13:07 +0000
                Re: Contradiction of bijections as a measure for infinite sets Richard Damon <richard@damon-family.org> - 2024-04-04 09:22 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-05 08:56 +0000
                Re: Contradiction of bijections as a measure for infinite sets Richard Damon <richard@damon-family.org> - 2024-04-05 07:32 -0400
                Re: Contradiction of bijections as a measure for infinite sets Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-04-05 19:30 -0700
                Re: Contradiction of bijections as a measure for infinite sets Tom Bola <Tom@bolamail.etc> - 2024-04-04 15:40 +0200
                Re: Contradiction of bijections as a measure for infinite sets FromTheRafters <FTR@nomail.afraid.org> - 2024-04-05 08:57 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-06 13:26 +0000
                Re: Contradiction of bijections as a measure for infinite sets Richard Damon <richard@damon-family.org> - 2024-04-06 09:40 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-06 13:55 +0000
                Re: Contradiction of bijections as a measure for infinite sets Richard Damon <richard@damon-family.org> - 2024-04-06 09:58 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-06 19:40 +0000
                Re: Contradiction of bijections as a measure for infinite sets Richard Damon <richard@damon-family.org> - 2024-04-06 16:03 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-07 08:32 +0000
                Re: Contradiction of bijections as a measure for infinite sets Richard Damon <richard@damon-family.org> - 2024-04-07 07:16 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-07 13:23 +0000
                how Richard Damon <richard@damon-family.org> - 2024-04-07 13:56 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-08 13:44 +0000
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-08 19:22 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-09 12:16 +0000
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-09 16:00 -0700
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-09 16:02 -0700
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-09 19:06 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-10 18:03 +0000
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-10 19:04 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-11 12:03 +0000
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-11 18:32 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-12 13:40 +0000
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-12 09:58 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-12 14:37 +0000
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-12 10:56 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-10 20:14 +0000
                Re: how FromTheRafters <FTR@nomail.afraid.org> - 2024-04-10 18:47 -0400
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-10 19:05 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-11 12:07 +0000
                Re: how Jim Burns <james.g.burns@att.net> - 2024-04-11 13:36 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-12 13:18 +0000
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-12 15:56 +0200
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-12 14:32 +0000
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-12 16:38 +0200
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-12 16:40 +0200
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-12 14:44 +0000
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-12 10:57 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-12 15:22 +0000
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-12 17:43 +0200
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-12 11:47 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-12 16:35 +0000
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-12 12:58 -0400
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-12 13:14 -0700
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-12 17:00 +0200
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-12 15:26 +0000
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-12 17:51 +0200
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-12 16:40 +0000
                Re: how Tom Bola <Tom@bolamail.etc> - 2024-04-12 18:44 +0200
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-12 13:16 -0700
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-12 13:04 -0700
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-12 13:03 -0700
                Re: how Jim Burns <james.g.burns@att.net> - 2024-04-12 14:57 -0400
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-11 21:16 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-12 13:45 +0000
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-12 10:02 -0400
                Re: how WM <wolfgang.mueckenheim@tha.de> - 2024-04-12 14:40 +0000
                Re: how Richard Damon <richard@damon-family.org> - 2024-04-12 11:01 -0400
                Re: how "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-10 18:16 -0700
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-04-03 19:48 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-04 09:43 +0000
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-04-04 13:03 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-05 09:06 +0000
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-04-05 15:03 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-06 13:44 +0000
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-04-06 13:49 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-06 19:49 +0000
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-04-07 17:47 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-08 13:55 +0000
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-04-08 21:54 -0400
                Re: Contradiction of bijections as a measure for infinite sets Moebius <moebius@example.invalid> - 2024-04-09 04:48 +0200
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-04-09 23:46 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-09 12:22 +0000
                Re: Contradiction of bijections as a measure for infinite sets Tom Bola <Tom@bolamail.etc> - 2024-04-09 14:47 +0200
                Re: Contradiction of bijections as a measure for infinite sets Moebius <moebius@example.invalid> - 2024-04-09 15:03 +0200
                Re: Contradiction of bijections as a measure for infinite sets Tom Bola <Tom@bolamail.etc> - 2024-04-09 17:15 +0200
                Re: Contradiction of bijections as a measure for infinite sets Moebius <moebius@example.invalid> - 2024-04-09 18:44 +0200
                Re: Contradiction of bijections as a measure for infinite sets "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-09 15:49 -0700
                Re: Contradiction of bijections as a measure for infinite sets Moebius <moebius@example.invalid> - 2024-04-09 15:04 +0200
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-04-09 16:27 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-10 17:57 +0000
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-04-10 16:13 -0400
                Re: Contradiction of bijections as a measure for infinite sets Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-04-10 17:39 -0700
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-04-11 11:16 -0400
                Re: Contradiction of bijections as a measure for infinite sets Richard Damon <richard@damon-family.org> - 2024-04-09 18:42 -0400
                Re: Contradiction of bijections as a measure for infinite sets "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-09 15:59 -0700
                Re: Contradiction of bijections as a measure for infinite sets Moebius <moebius@example.invalid> - 2024-04-10 05:37 +0200
                Re: Contradiction of bijections as a measure for infinite sets "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-10 11:47 -0700
                Re: Contradiction of bijections as a measure for infinite sets "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-04-09 15:47 -0700
                Re: Contradiction of bijections as a measure for infinite sets "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-31 13:20 -0700
                Re: Contradiction of bijections as a measure for infinite sets Richard Damon <richard@damon-family.org> - 2024-03-27 20:52 -0400
              Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-26 13:24 +0000
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-03-26 13:04 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-27 13:46 +0000
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-03-27 15:10 -0400
                Re: Contradiction of bijections as a measure for infinite sets "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-27 13:57 -0700
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-03-27 18:50 -0400
                Re: Contradiction of bijections as a measure for infinite sets Richard Damon <richard@damon-family.org> - 2024-03-26 21:19 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-27 13:57 +0000
                Re: Contradiction of bijections as a measure for infinite sets Richard Damon <richard@damon-family.org> - 2024-03-27 20:57 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-28 20:00 +0000
                Re: Contradiction of bijections as a measure for infinite sets Richard Damon <richard@damon-family.org> - 2024-03-29 09:31 -0400
    Re: Contradiction of bijections as a measure for infinite sets Richard Damon <richard@damon-family.org> - 2024-03-24 17:09 -0400
      Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-25 11:15 +0000
        Re: Contradiction of bijections as a measure for infinite sets Richard Damon <richard@damon-family.org> - 2024-03-25 07:29 -0400
          Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-25 21:49 +0000
    Re: Contradiction of bijections as a measure for infinite sets FromTheRafters <FTR@nomail.afraid.org> - 2024-03-24 17:10 -0400
      Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-25 11:20 +0000
        Re: Contradiction of bijections as a measure for infinite sets FromTheRafters <FTR@nomail.afraid.org> - 2024-03-25 14:31 -0400
          Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-25 21:53 +0000
            Re: Contradiction of bijections as a measure for infinite sets FromTheRafters <FTR@nomail.afraid.org> - 2024-03-25 18:49 -0400
              Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-26 13:18 +0000
                Re: Contradiction of bijections as a measure for infinite sets FromTheRafters <FTR@nomail.afraid.org> - 2024-03-26 09:39 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-26 13:47 +0000
                Re: Contradiction of bijections as a measure for infinite sets FromTheRafters <FTR@nomail.afraid.org> - 2024-03-26 14:04 -0400
                Re: Contradiction of bijections as a measure for infinite sets Phil Carmody <pc+usenet@asdf.org> - 2024-03-26 23:12 +0200
                Re: Contradiction of bijections as a measure for infinite sets FromTheRafters <FTR@nomail.afraid.org> - 2024-03-26 17:40 -0400
                Re: Contradiction of bijections as a measure for infinite sets "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-26 19:43 -0700
                Re: Contradiction of bijections as a measure for infinite sets Phil Carmody <pc+usenet@asdf.org> - 2024-03-27 13:35 +0200
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-27 13:48 +0000
                Re: Contradiction of bijections as a measure for infinite sets FromTheRafters <FTR@nomail.afraid.org> - 2024-03-27 11:23 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-27 21:50 +0000
                Re: Contradiction of bijections as a measure for infinite sets FromTheRafters <FTR@nomail.afraid.org> - 2024-03-27 19:37 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-28 19:55 +0000
                Re: Contradiction of bijections as a measure for infinite sets FromTheRafters <FTR@nomail.afraid.org> - 2024-03-28 18:11 -0400
                Re: Contradiction of bijections as a measure for infinite sets Richard Damon <richard@damon-family.org> - 2024-03-29 13:05 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-30 16:05 +0000
                Re: Contradiction of bijections as a measure for infinite sets Richard Damon <richard@damon-family.org> - 2024-03-30 13:48 -0400
                Re: Contradiction of bijections as a measure for infinite sets Richard Damon <richard@damon-family.org> - 2024-03-27 20:59 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-28 19:57 +0000
                Re: Contradiction of bijections as a measure for infinite sets Richard Damon <richard@damon-family.org> - 2024-03-29 13:07 -0400
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-03-28 17:25 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-28 21:40 +0000
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-03-28 18:30 -0400
                Re: Contradiction of bijections as a measure for infinite sets "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-28 17:54 -0700
                Re: Contradiction of bijections as a measure for infinite sets "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-28 18:00 -0700
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-03-29 05:46 -0400
                Re: Contradiction of bijections as a measure for infinite sets "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-29 15:53 -0700
                Re: Contradiction of bijections as a measure for infinite sets Tom Bola <Tom@bolamail.etc> - 2024-03-29 15:13 +0100
                Re: Contradiction of bijections as a measure for infinite sets "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-29 15:52 -0700
                Re: Contradiction of bijections as a measure for infinite sets Tom Bola <Tom@bolamail.etc> - 2024-03-30 00:29 +0100
                Re: Contradiction of bijections as a measure for infinite sets "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-29 16:31 -0700
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-03-30 09:56 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-30 16:17 +0000
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-03-30 15:04 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-31 12:20 +0000
                Re: Contradiction of bijections as a measure for infinite sets Tom Bola <Tom@bolamail.etc> - 2024-03-31 15:19 +0200
                Re: Contradiction of bijections as a measure for infinite sets Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-03-31 08:10 -0700
                Re: Contradiction of bijections as a measure for infinite sets Tom Bola <Tom@bolamail.etc> - 2024-03-31 17:31 +0200
                Re: Contradiction of bijections as a measure for infinite sets Ross Finlayson <ross.a.finlayson@gmail.com> - 2024-03-31 14:10 -0700
                Re: Contradiction of bijections as a measure for infinite sets Tom Bola <Tom@bolamail.etc> - 2024-03-31 17:38 +0200
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-03-31 13:38 -0400
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-03-31 15:37 -0400
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-03-31 15:43 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-01 15:34 +0000
                Re: Contradiction of bijections as a measure for infinite sets Moebius <moebius@example.invalid> - 2024-04-01 20:11 +0200
                Re: Contradiction of bijections as a measure for infinite sets Moebius <moebius@example.invalid> - 2024-04-01 20:14 +0200
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-04-01 14:34 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-02 07:32 +0000
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-04-02 11:35 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-03 13:29 +0000
                Re: Contradiction of bijections as a measure for infinite sets Jim Burns <james.g.burns@att.net> - 2024-04-03 17:07 -0400
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-30 16:09 +0000
                Re: Contradiction of bijections as a measure for infinite sets Moebius <moebius@example.invalid> - 2024-03-31 19:14 +0200
                Re: Contradiction of bijections as a measure for infinite sets "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2024-03-31 13:22 -0700
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-01 15:30 +0000
                Re: Contradiction of bijections as a measure for infinite sets Moebius <moebius@example.invalid> - 2024-04-01 20:26 +0200
                Re: Contradiction of bijections as a measure for infinite sets Moebius <moebius@example.invalid> - 2024-04-01 22:41 +0200
                Re: Contradiction of bijections as a measure for infinite sets Tom Bola <Tom@bolamail.etc> - 2024-03-29 15:09 +0100
                Re: Contradiction of bijections as a measure for infinite sets Tom Bola <Tom@bolamail.etc> - 2024-03-29 17:31 +0100
                Re: Contradiction of bijections as a measure for infinite sets Moebius <moebius@example.invalid> - 2024-03-31 19:17 +0200
                Re: Contradiction of bijections as a measure for infinite sets Tom Bola <Tom@bolamail.etc> - 2024-03-31 19:37 +0200
                Re: Contradiction of bijections as a measure for infinite sets Tom Bola <Tom@bolamail.etc> - 2024-03-31 19:44 +0200
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-03-30 16:24 +0000
                Re: Contradiction of bijections as a measure for infinite sets Tom Bola <Tom@bolamail.etc> - 2024-03-30 17:37 +0100
                Re: Contradiction of bijections as a measure for infinite sets Moebius <moebius@example.invalid> - 2024-03-31 03:57 +0200
                Re: Contradiction of bijections as a measure for infinite sets Moebius <moebius@example.invalid> - 2024-04-05 22:07 +0200
                Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-06 13:47 +0000
    Re: Contradiction of bijections as a measure for infinite sets Moebius <moebius@example.invalid> - 2024-03-30 23:53 +0100
      Re: Contradiction of bijections as a measure for infinite sets WM <wolfgang.mueckenheim@tha.de> - 2024-04-01 15:04 +0000
        Re: Contradiction of bijections as a measure for infinite sets Moebius <moebius@example.invalid> - 2024-04-01 20:37 +0200
          Re: Contradiction of bijections as a measure for infinite sets Tom Bola <Tom@bolamail.etc> - 2024-04-01 20:47 +0200
            Re: Contradiction of bijections as a measure for infinite sets Moebius <moebius@example.invalid> - 2024-04-01 20:52 +0200
  Re: V FromTheRafters <FTR@nomail.afraid.org> - 2024-03-24 17:03 -0400
    Re: V Dieter Heidorn <d.heidorn@t-online.de> - 2024-03-24 22:09 +0100
      Re: V FromTheRafters <FTR@nomail.afraid.org> - 2024-03-24 17:18 -0400

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