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Re: The mathematical constraints of set theory

From Ben Bacarisse <ben.usenet@bsb.me.uk>
Newsgroups sci.math
Subject Re: The mathematical constraints of set theory
Date 2023-06-16 01:44 +0100
Organization A noiseless patient Spider
Message-ID <87ttv8nsl6.fsf@bsb.me.uk> (permalink)
References <885f11ce-f96b-4c21-8aa3-98bdb0cf867bn@googlegroups.com> <87352urtld.fsf@bsb.me.uk> <07e5dbd5-0792-445c-a7dc-9e614474ac52n@googlegroups.com>

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WM <askasker48@gmail.com> writes:
(AKA Dr. Wolfgang Mückenheim or Mueckenheim who teaches "Geschichte des 
Unendlichen" at Hochschule Augsburg.) 

> Ben Bacarisse schrieb am Mittwoch, 14. Juni 2023 um 16:45:12 UTC+2:
>> Peter Peters <pp15...@gmail.com> writes: 

>> > 1) As long as the sequence of endsegments has not decreased completely 
>> > to the empty set, the remaining contents is in all endsegments. This 
>> > must be denied.
>> Since sets don't change, "remaining" is a magic word.
> The sequence consist of different terms. They change.

No.  Nothing changes.  Sets in WM change, which I why you admitted that
you can't define set membership, equality and difference in WMaths.  But
in mathematics, sets, sequences and terms in sequences don't change.
This is one of the magic words you like to use.

>  > You might mean 
>> 
>> ∀n,m, m ≥ n -> es(n) ⊆ es(m). 
>
> The other way round.
>
>> > 2) As long as infinitely many, i.e., almost all natural numbers are 
>> > the contents of endsegments, there can only be a finite set of 
>> > endsegments. This must be denied.
>> Hmm... Can't parse this.
>
> 1, 2, 3, ..., n-1, n, |, n, n+1, ...
>
> The contents follows upon "|". An infinte contents of all endsegments
> prevents an infinite set of indices.

Try using mathematics.  The notation exists for a reason.

>> > 3) Every lossless exchange is lossless. This must be denied.
>
> See Jim Burns.

Good to see that you agree with him about this.

>> > 4) Infinitely many unit fractions cannot sit below all x > 0. This 
>> > must be denied.
>>
>> Clever vague use of "all". You know perfectly well the two facts you 
>> are trying to conflate here. They are: 
>> 
>> ∀x > 0, |{n ∈ N | 1/n < x}| = ℵ₀ 
>
> Impossible because as x you could choose (if not dark) the third unit
> fraction which must exist if there are infinitely many.

No.  Proofs don't work by assertion.  There is no third (smallest) unit
fraction.

>> > 5) There are more nodes than path in the Binary Tree because all paths 
>> > must be distinguished by nodes. This must be denied.
>
>> I.e. that there are "more" functions from N to {0,1} than there are 
>> natural numbers.
>
> No.

Apparently (in another reply) you agree.  2 out of five is good.  Well done.

-- 
Ben.

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The mathematical constraints of set theory Peter Peters <pp1585024@gmail.com> - 2023-06-14 03:35 -0700
  Re: The mathematical constraints of set theory Guckie <alberstein@freenet.de> - 2023-06-14 16:36 +0300
    Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-14 07:45 -0700
      Re: The mathematical constraints of set theory Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-14 08:20 -0700
      Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-14 16:30 +0100
        Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-14 11:45 -0700
          Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-14 22:13 +0100
            Re: The mathematical constraints of set theory Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-14 18:07 -0700
              Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-15 06:24 -0700
            Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-15 05:50 -0700
              Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-15 17:36 +0100
        Re: The mathematical constraints of set theory Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-14 13:51 -0700
          Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-14 22:19 +0100
      Re: The mathematical constraints of set theory "Socratis T.n.p." <andreasorrentino128@gmail.com> - 2023-06-23 04:44 -0700
        Re: The mathematical constraints of set theory "Socratis T.n.p." <andreasorrentino128@gmail.com> - 2023-06-23 10:39 -0700
        Re: The mathematical constraints of set theory "Socratis T.n.p." <andreasorrentino128@gmail.com> - 2023-06-27 09:00 -0700
    Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-15 06:13 -0700
  Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-14 15:45 +0100
    Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-14 10:08 -0700
      Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-16 01:44 +0100
        Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-16 08:03 -0700
          Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-16 08:29 -0700
            Re: The mathematical constraints of set theory Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-16 09:03 -0700
            Re: The mathematical constraints of set theory FromTheRafters <FTR@nomail.afraid.org> - 2023-06-16 13:30 -0400
              Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-16 12:08 -0700
            Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-17 06:26 -0700
              Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-17 09:18 -0700
                Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-18 05:57 -0700
                Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-18 07:01 -0700
                Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-19 06:13 -0700
              Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-17 10:09 -0700
                Re: The mathematical constraints of set theory Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-17 10:58 -0700
                Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-18 06:09 -0700
                Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-18 09:40 -0700
                Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-19 05:05 -0700
                Re: The mathematical constraints of set theory Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-19 06:15 -0700
                Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-19 06:22 -0700
                Re: The mathematical constraints of set theory Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-19 06:38 -0700
                Re: The mathematical constraints of set theory Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-19 06:40 -0700
                Re: The mathematical constraints of set theoryn Timothy Golden <timbandtech@gmail.com> - 2023-06-19 08:24 -0700
                Re: The mathematical constraints of set theoryn Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-19 09:11 -0700
                Re: The mathematical constraints of set theoryn Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-19 11:27 -0700
                Re: The mathematical constraints of set theoryn Timothy Golden <timbandtech@gmail.com> - 2023-06-19 11:44 -0700
                Re: The mathematical constraints of set theoryn Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-19 12:07 -0700
                Re: The mathematical constraints of set theoryn Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-19 12:12 -0700
                Re: The mathematical constraints of set theoryn Timothy Golden <timbandtech@gmail.com> - 2023-06-20 06:43 -0700
                Re: The mathematical constraints of set theoryn Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-20 06:53 -0700
                Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-19 16:47 +0100
                Re: The mathematical constraints of set theory Dieter Heidorn <d.heidorn@t-online.de> - 2023-06-19 20:11 +0200
                Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-20 00:08 +0100
                Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-20 08:49 -0700
                Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-23 02:35 +0100
                Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-23 10:09 -0700
                Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-23 10:19 -0700
                Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-26 01:13 +0100
                Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-25 18:35 -0700
                Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-26 03:04 +0100
                Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-25 19:52 -0700
                Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-25 19:54 -0700
                Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-26 15:42 +0100
                Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-27 08:39 -0700
                Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-28 02:43 +0100
                Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-28 04:32 -0700
                Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-28 15:16 +0100
                Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-28 07:48 -0700
                Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-28 16:43 +0100
                Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-28 09:49 -0700
                Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-06-29 09:59 -0400
                Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-30 13:04 -0700
                Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-06-30 18:09 -0400
                Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-30 15:18 -0700
                Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-30 15:25 -0700
                Re: The mathematical constraints of set theory FromTheRafters <FTR@nomail.afraid.org> - 2023-06-30 18:53 -0400
                Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-30 16:42 -0700
                Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-01 10:19 -0700
                Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-07-01 14:06 -0400
                Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-02 07:52 -0700
                Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-07-02 09:48 -0700
                Re: The mathematical constraints of set theory Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-07-02 10:39 -0700
                Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-07-02 13:45 -0700
                Re: The mathematical constraints of set theory Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-07-02 14:09 -0700
                Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-07-02 14:08 -0400
                Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-03 07:01 -0700
                Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-07-03 13:09 -0400
                Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-04 08:33 -0700
                Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-07-04 18:43 -0400
                Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-05 02:50 -0700
                Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-07-05 10:39 -0400
                Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-05 08:45 -0700
                Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-07-05 13:14 -0400
                Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-07-06 06:27 -0700
                Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-09 06:41 -0700
                Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-07-09 07:58 -0700
                Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-10 02:40 -0700
                Re: The mathematical constraints of set theory Tom Bola <Tom@bolamail.etc> - 2023-07-01 20:23 +0200
                Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-01 11:44 -0700
                Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-02 07:43 -0700
                Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-02 08:42 -0700
                Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-03 06:52 -0700
                Re: The mathematical constraints of set theory "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2023-07-01 11:56 -0700
                Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-28 09:34 -0700
                Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-25 20:21 -0700
                Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-28 09:46 -0700
                Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-19 08:11 -0700
                Re: The mathematical constraints of set theory Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-19 08:20 -0700
                Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-19 06:18 -0700
                Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-19 07:12 -0700
                Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-20 08:45 -0700
                Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-20 10:38 -0700
                Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-20 14:39 -0700
                Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-18 06:04 -0700
                Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-06-19 09:34 -0400
                Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-20 08:44 -0700
                Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-06-20 13:31 -0400
                Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-20 14:37 -0700
                Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-20 15:03 -0700
                Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-20 15:05 -0700
                Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-21 06:53 -0700
                Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-21 06:50 -0700
                Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-21 07:37 -0700
                Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-22 06:13 -0700
                Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-06-20 20:34 -0400
                Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-21 06:59 -0700
                Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-06-21 11:58 -0400
                Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-22 06:19 -0700
                Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-06-22 12:30 -0400
                Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-22 10:38 -0700
                Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-22 20:18 -0700
                Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-23 10:06 -0700
                Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-23 10:17 -0700
                Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-23 10:24 -0700
    Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-15 06:16 -0700
      Re: The mathematical constraints of set theory Gus Gassmann <horand.gassmann@gmail.com> - 2023-06-15 09:50 -0700
        Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-15 14:00 -0700
      Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-16 01:28 +0100
        Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-16 07:50 -0700
          Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-18 02:13 +0100
            Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-18 06:19 -0700
              Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-20 01:26 +0100
                Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-20 07:09 -0700
                Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-20 15:38 +0100
                Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-20 12:32 -0700
                Re: The mathematical constraints of set theory "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2023-06-20 14:05 -0700
                Re: The mathematical constraints of set theory Timothy Golden <timbandtech@gmail.com> - 2023-06-21 04:43 -0700
                Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-20 14:33 -0700
                Re: The mathematical constraints of set theory Ben Bacarisse <ben.usenet@bsb.me.uk> - 2023-06-23 02:56 +0100
          Re: The mathematical constraints of set theory "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2023-06-17 18:34 -0700
  Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-06-14 16:50 -0700
  Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-06-14 20:19 -0400
  Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-06-15 17:08 -0400
    Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-06-16 07:45 -0700
      Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-06-16 14:58 -0400
  Re: The mathematical constraints of set theory Jim Burns <james.g.burns@att.net> - 2023-06-15 18:56 -0400
  Re: The mathematical constraints of set theory Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2023-06-19 08:37 -0700
  Re: The mathematical constraints of set theory Archimedes Plutonium <plutonium.archimedes@gmail.com> - 2023-06-23 11:16 -0700
  Re: The mathematical constraints of set theory "zelos...@gmail.com" <zelos.malum@gmail.com> - 2023-07-05 00:23 -0700
    Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-05 02:54 -0700
      Re: The mathematical constraints of set theory "zelos...@gmail.com" <zelos.malum@gmail.com> - 2023-07-05 09:36 -0700
        Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-06 05:29 -0700
          Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-09 08:09 -0700
            Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-10 02:42 -0700
              Re: The mathematical constraints of set theory Gus Gassmann <horand.gassmann@gmail.com> - 2023-07-10 04:14 -0700
                Re: The mathematical constraints of set theory WM <askasker48@gmail.com> - 2023-07-10 07:27 -0700
                Re: The mathematical constraints of set theory Gus Gassmann <horand.gassmann@gmail.com> - 2023-07-10 07:57 -0700
  Re: The mathematical constraints of set theory Fritz Feldhase <franz.fritschee.ff@gmail.com> - 2023-07-05 07:48 -0700

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