Re: Cardinalities of sets

From	wm <wolfgang.mueckenheim@tha.de>
Newsgroups	sci.math
Subject	Re: Cardinalities of sets
Date	2026-02-23 16:51 +0100
Organization	tha
Message-ID	<10nht2s$maqj$1@solani.org> (permalink)
References	(9 earlier) <10nfp4m$2v3k$1@news.muc.de> <10nft68$2ffnm$1@dont-email.me> <10nfuo1$2gur$1@news.muc.de> <10nhhcl$2voth$1@dont-email.me> <10nhlla$2a2o$1@news.muc.de>

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Am 23.02.2026 um 14:45 schrieb Alan Mackenzie:
> WM <wolfgang.mueckenheim@tha.de> wrote:
>> Am 22.02.2026 um 23:08 schrieb Alan Mackenzie:
>>> WM <wolfgang.mueckenheim@tha.de> wrote:
>>>> Am 22.02.2026 um 21:32 schrieb Alan Mackenzie:
>>>>> wm <wolfgang.mueckenheim@tha.de> wrote:
>>>>>> Am 21.02.2026 um 17:11 schrieb Ross Finlayson:
> 
>>>>>>> Cardinality establishes a transitive inequality among sets,
>>>>>>> where "cardinals" themselves as equivalence classes of sets
>>>>>>> having any transitive bijective relation, are, besides zero,
>>>>>>> rather too large to be sets in ordinary set theories like ZF(C).
> 
>>>>>> Cardinality is nonsense. It shows a countable result when potential
>>>>>> infinity is used but is greater when actual infinity is used.
> 
>>>>> More like "potential infinity" and "actual infinity" are nonsense.
> 
>>>> Not everything you cannot comprehend is nonsense.
> 
>>> I understand that "potential infinity" and "actual infinity" are not
>>> parts of modern mathematics.  You appear not to.
> 
>> I understand that these deeper notions are prohibited by the leading
>> swindlers because they know that this knowledge disproves set theory.
> 
> This is a newsgroup for mathematics, not conspiracy theories.

Mathematics unfortunately has becomen degraded this way. It is 
impossible that the brighter leaders don't understand the mistakes of 
set theory. Even the avarage mathematician knows that every indiviudelly 
chosen number has more successors than predecessors, such that at least 
half of all natural numbers cannot be applied individuzally. But kind of 
Freudian repression prevents most to understand that the whole set ℕ can 
only be manipiulated collectively. Most numbers are dark such that 
Dedekin-Cantor's way of enumerating the algebraics must break down.
> 
>> Potential infinity is used to enumerate the fractions, the algebraics,
>> the prime numbers. Very different multitudes. But the potentially
>> infinite sequence of natural numbers is very elastic. Example: After
>> enumerating the positive fractions it can also absorb all negative
>> fractions.
> 
> Not really.  There is no "after" enumerating the positive fractions.

Cantor enumerates the positive fractions. Then inserts each negative 
fraction behind the positive fraction. Please try to learn the stuff 
before you play the expert.

>> Actual infinity is used to construct Cantors list which is too rigid to
>> absorb even one further number, namely the antidiagonal number.
> 
> "Actual infinity", whatever that might mean, is in no way "used" to
> construct Cantor's non-existent list.

Please try to learn the stuff before you play the expert.
The list is considered complete by using all natural numbers for 
enumerating the entries.

> Lists don't "absorb" numbers,
> whatever that might mean.

Hilbert's hotel can absorb another guest.

> Cantor showed that any such purported
> complete list was in fact not complete, by constructing a number not in
> the list.

He claims that the enumeration is complete, and no new guest can be 
absorbed.

Regards, WM

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Cardinalities of sets (was: energy and mass) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-02-21 16:16 +0100
  Re: Cardinalities of sets Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-21 08:11 -0800
    Cardinalities of sets wm <wolfgang.mueckenheim@tha.de> - 2026-02-22 19:04 +0100
      Re: Cardinalities of sets Alan Mackenzie <acm@muc.de> - 2026-02-22 20:32 +0000
        Re: Cardinalities of sets WM <wolfgang.mueckenheim@tha.de> - 2026-02-22 22:41 +0100
          Re: Cardinalities of sets Alan Mackenzie <acm@muc.de> - 2026-02-22 22:08 +0000
            Re: Cardinalities of sets Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-22 21:07 -0800
            Re: Cardinalities of sets WM <wolfgang.mueckenheim@tha.de> - 2026-02-23 13:32 +0100
              Re: Cardinalities of sets Alan Mackenzie <acm@muc.de> - 2026-02-23 13:45 +0000
                Re: Cardinalities of sets wm <wolfgang.mueckenheim@tha.de> - 2026-02-23 16:51 +0100
                Re: Cardinalities of sets Alan Mackenzie <acm@muc.de> - 2026-02-23 17:16 +0000
                Re: Cardinalities of sets WM <wolfgang.mueckenheim@tha.de> - 2026-02-23 18:27 +0100
                Re: Cardinalities of sets Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-23 09:38 -0800
                Re: Cardinalities of sets Alan Mackenzie <acm@muc.de> - 2026-02-23 21:10 +0000
                Re: Cardinalities of sets wm <wolfgang.mueckenheim@tha.de> - 2026-02-24 19:33 +0100
                Re: Cardinalities of sets Alan Mackenzie <acm@muc.de> - 2026-02-25 12:52 +0000
                Re: Cardinalities of sets WM <wolfgang.mueckenheim@tha.de> - 2026-02-25 21:28 +0100
                Re: Cardinalities of sets Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-26 08:59 -0800
                Re: Cardinalities of sets wm <wolfgang.mueckenheim@tha.de> - 2026-02-24 18:40 +0100
  Re: Cardinalities of sets Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-21 08:14 -0800
    Re: Cardinalities of sets Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-21 08:30 -0800
      Re: Cardinalities of sets Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-21 08:51 -0800
        Re: Cardinalities of sets Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-03-19 20:59 -0700
  Cardinalities of sets wm <wolfgang.mueckenheim@tha.de> - 2026-02-22 18:55 +0100
    Re: Cardinalities of sets Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-02-22 22:52 +0100
      Re: Cardinalities of sets WM <wolfgang.mueckenheim@tha.de> - 2026-02-23 13:24 +0100
        Re: Cardinalities of sets Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-02-23 23:41 +0100
          Re: Cardinalities of sets wm <wolfgang.mueckenheim@tha.de> - 2026-02-24 18:46 +0100
            Re: Cardinalities of sets Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-02-25 18:10 +0100
              Re: Cardinalities of sets WM <wolfgang.mueckenheim@tha.de> - 2026-02-25 21:32 +0100
                Re: Cardinalities of sets Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-02-26 00:36 +0100
                Re: Cardinalities of sets "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-02-26 01:10 -0800
                Re: Cardinalities of sets WM <wolfgang.mueckenheim@tha.de> - 2026-02-26 16:36 +0100
                Re: Cardinalities of sets Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-02-26 22:46 +0100
                Re: Cardinalities of sets Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-26 18:08 -0800
                Re: Cardinalities of sets WM <wolfgang.mueckenheim@tha.de> - 2026-02-27 16:52 +0100
                Re: Cardinalities of sets Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-02-28 00:39 +0100
                Re: Cardinalities of sets Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-27 20:03 -0800
                Re: Cardinalities of sets Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-02-27 20:12 -0800
                Re: Cardinalities of sets Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-03-01 08:12 -0800
                Re: Cardinalities of sets Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-03-04 10:15 -0800
                Re: Cardinalities of sets WM <wolfgang.mueckenheim@tha.de> - 2026-02-28 19:29 +0100
                Re: Cardinalities of sets Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-03-17 15:57 +0100
                Re: Cardinalities of sets WM <wolfgang.mueckenheim@tha.de> - 2026-03-17 18:11 +0100
                Re: Cardinalities of sets Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-03-17 14:54 -0700

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