Re: Replacement of Cardinality

Liste des GroupesRevenir à math 
Sujet : Re: Replacement of Cardinality
De : wolfgang.mueckenheim (at) *nospam* tha.de (WM)
Groupes : sci.logic sci.math
Date : 22. Aug 2024, 12:17:25
Autres entêtes
Organisation : Nemoweb
Message-ID : <bujhfRmCrhbrenSju9nN_R0bHhY@jntp>
References : 1 2 3 4 5 6 7 8 9 10
User-Agent : Nemo/0.999a
Le 21/08/2024 à 20:20, Jim Burns a écrit :
On 8/21/2024 6:43 AM, WM wrote:
Le 20/08/2024 à 22:05, Jim Burns a écrit :
 
No min.⅟ℕᵈᵉᶠ exists.
>
The reason is potential infinity.
 Is potentialᵂᴹ.infinity mathematicsᵂᴹ?
All of classical mathematics is embedded into potential infinity.
 Judging from your edicts on this topic,
the answer looks to be both 'yes' and 'no'.
I am interested in actual infinity. We cannot prove its existence but only apply logic like this: If a complete chain exists which does not continue into the negative, then it ends before. Either at one or at more members. The latter is excluded by ∀n ∈ ℕ: 1/n - 1/(n+1) > 0 .
  We are agreed, though, that
no min.⅟ℕᵈᵉᶠ exists.
Of course. After each one there will appear more. Choose the smallest one you can, recognize that there are many more following.
 It follows that ⅟ℕᵈᵉᶠ has properties that
the unit.fractionsᵈᵉᶠ > x > 0
don't have.
There is no set ℕᵈᵉᶠ because of lacking completeness. Sets of set theory are complete.
Regards, WM

Date Sujet#  Auteur
19 Aug 24 * Re: Replacement of Cardinality25Jim Burns
19 Aug 24 +* Re: Replacement of Cardinality23Moebius
19 Aug 24 i+* Re: Replacement of Cardinality16Jim Burns
19 Aug 24 ii+- Re: Replacement of Cardinality1Moebius
20 Aug 24 ii`* Re: Replacement of Cardinality14WM
20 Aug 24 ii `* Re: Replacement of Cardinality13Jim Burns
21 Aug 24 ii  +* Re: Replacement of Cardinality4Moebius
21 Aug 24 ii  i`* Re: Replacement of Cardinality3WM
21 Aug 24 ii  i `* Re: Replacement of Cardinality2Richard Damon
21 Aug 24 ii  i  `- Re: Replacement of Cardinality1WM
21 Aug 24 ii  `* Re: Replacement of Cardinality8WM
21 Aug 24 ii   +- Re: Replacement of Cardinality1Richard Damon
21 Aug 24 ii   `* Re: Replacement of Cardinality6Jim Burns
22 Aug 24 ii    `* Re: Replacement of Cardinality5WM
22 Aug 24 ii     +* Re: Replacement of Cardinality3Python
22 Aug 24 ii     i`* Re: Replacement of Cardinality2WM
22 Aug 24 ii     i `- Re: Replacement of Cardinality1Python
22 Aug 24 ii     `- Re: Replacement of Cardinality1Jim Burns
19 Aug 24 i+* Re: Replacement of Cardinality5Chris M. Thomasson
19 Aug 24 ii+* Re: Replacement of Cardinality3Chris M. Thomasson
19 Aug 24 iii`* Re: Replacement of Cardinality2FromTheRafters
20 Aug 24 iii `- Re: Replacement of Cardinality1Chris M. Thomasson
19 Aug 24 ii`- Re: Replacement of Cardinality1FromTheRafters
20 Aug 24 i`- Re: Replacement of Cardinality1WM
20 Aug 24 `- Re: Replacement of Cardinality1WM

Haut de la page

Les messages affichés proviennent d'usenet.

NewsPortal