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Re: Cardinalities of sets

From WM <wolfgang.mueckenheim@tha.de>
Newsgroups sci.math
Subject Re: Cardinalities of sets
Date 2026-03-17 18:11 +0100
Organization A noiseless patient Spider
Message-ID <10pc1vr$33n0f$1@dont-email.me> (permalink)
References (22 earlier) <10nqevl$1d2dp$1@gwaiyur.mb-net.net> <10nsej8$2l0v4$1@dont-email.me> <10nt9v1$1kapn$1@gwaiyur.mb-net.net> <10nvc6s$3j4sp$1@dont-email.me> <10pbq5c$nc3v$1@gwaiyur.mb-net.net>

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Am 17.03.2026 um 15:57 schrieb Thomas 'PointedEars' Lahn:
> WM wrote:
>> Am 28.02.2026 um 00:39 schrieb Thomas 'PointedEars' Lahn:
>>> WM wrote:
>>>> By the way, closed formula or not: The fractioons are not countable.
>>>> Every intelligent mathematician can understand my proof:
>>
>>>> According to Cantor all positive fractions
>>>>
>>>>        1/1, 1/2, 1/3, 1/4, ...
>>>>        2/1, 2/2, 2/3, 2/4, ...
>>>>        3/1, 3/2, 3/3, 3/4, ...
>>>>        4/1, 4/2, 4/3, 4/4, ...
>>>>        ...
>>>>
>>>> can be indexed by the Cantor function k = (m + n - 1)(m + n - 2)/2 + m
>>>
>>> Again, that is your claim, not Cantor's.
>>
>> Es hat nämlich die Funktion  =  + (- 1)(- 2)/2, wie
>> leicht zu zeigen, die bemerkenswerte Eigenschaft, daß sie alle positiven
>> ganzen Zahlen und jede nur einmal darstellt, wenn in ihr 
>> undunabhängig voneinander ebenfalls jeden positiven, ganzzahligen
>> Wert erhalten [1]. [Cantor, Collected Works p. 132]
> 
> This purported quote is horribly broken,

Look it up yourself.

> and "Collected Works p. 132" is not
> a valid reference.

It is a reference for every mathematician.

> So both the quotation and the citation are useless.  Try
> again.

I am not in charge to improve your education.
> 
> In any case, you should be aware that even if you could provide evidence
> that Cantor wrote that *somewhere else*, that would not change the fact that
> he definitely did NOT write it in the 1883 letter to Lipschitz that you keep
> citing.

I told you already that he did not use his formula in that letter, but 
asked for a better one to describe the enumeration of the rational 
numbers, since he knew only the formula to enumerat the fractions.

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
                Re: Cardinalities of sets Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-03-22 01:19 +0100
                Re: Cardinalities of sets Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-03-21 18:24 -0700
                Re: Cardinalities of sets wm <wolfgang.mueckenheim@tha.de> - 2026-03-22 15:42 +0100
                Re: Cardinalities of sets Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-03-22 15:10 -0700
                Re: Cardinalities of sets Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-03-23 09:32 -0700
                Re: Cardinalities of sets Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2026-03-23 23:24 +0100
                Re: Cardinalities of sets wm <wolfgang.mueckenheim@tha.de> - 2026-03-24 20:44 +0100
                Re: Cardinalities of sets Maximilian Takashita <atiia@kiimia.jp> - 2026-03-23 20:18 +0000

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