Re: Replacement of Cardinality

Liste des GroupesRevenir à s logic 
Sujet : Re: Replacement of Cardinality
De : invalid (at) *nospam* example.invalid (Moebius)
Groupes : sci.logic sci.math
Date : 13. Aug 2024, 21:16:27
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Organisation : A noiseless patient Spider
Message-ID : <v9geur$2155$1@dont-email.me>
References : 1 2 3 4 5 6 7 8 9 10 11 12
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Am 13.08.2024 um 21:21 schrieb Chris M. Thomasson:
On 8/13/2024 7:27 AM, WM wrote:

... the smallest unit fractions ...
 This irks me a bit. The smallest unit fractions? How do you define them?
Consider a totally ordered set M, say ordered by <=.
Then if there is an element m in M such that for all elements x in M: m <= x, we call that element _the_ /smallest/ element in m. (Reason: There can only be ONE such element in M, if there is such an Element in M at all.)
By "the smallest unit fractions" WM is referring to the smalles unit fraction u_WM and some of the unit fractions which are slightly larger:
          u_WM < u_WM' < u_WM'' < ...
Though it is not quite clear how many of these unit fractions are considered "smallest unit fractions" by WM. The first 2, 3? Who knows?!
Mückenheim's World is a strange place.
Especialy, since there is not even ONE smallest unit fraction in mathematics.

Date Sujet#  Auteur
26 Jul 24 * Replacement of Cardinality712WM
26 Jul 24 +* Re: Replacement of Cardinality2joes
27 Jul 24 i`- Re: Replacement of Cardinality1WM
27 Jul 24 +* Re: Replacement of Cardinality67Richard Damon
27 Jul 24 i`* Re: Replacement of Cardinality66WM
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3 Aug 24 i         `* Re: Replacement of Cardinality2Mikko
3 Aug 24 i          `- Re: Replacement of Cardinality1WM
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28 Jul 24  +* Re: Replacement of Cardinality612WM
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