Re: how

Liste des GroupesRevenir à s math 
Sujet : Re: how
De : richard (at) *nospam* damon-family.org (Richard Damon)
Groupes : sci.math
Date : 24. Apr 2024, 02:50:22
Autres entêtes
Organisation : i2pn2 (i2pn.org)
Message-ID : <v09ogu$222fd$1@i2pn2.org>
References : 1 2 3 4 5 6 7 8 9 10 11
User-Agent : Mozilla Thunderbird
On 4/23/24 2:06 PM, WM wrote:
Le 22/04/2024 à 20:02, FromTheRafters a écrit :
WM has brought this to us :
Le 21/04/2024 à 00:44, FromTheRafters a écrit :
WM wrote :
>
What is a gap in the ordinals?
>
It is a not existing ordinal between two ordinals. It is a not existing natural number next to ω, for instance.
>
Sets do not have not existing elements.
>
What is ω - 1?
>
An absurdity.
 Not more nor less than ω.
 Regards, WM
But if ω - 1 existed, it would be before ω, and thus less than it.
That is the definition of ordinal numbers.
But since it is NOT a "finite" number, as "ω - 1" + 1 would be ω and not a finite number, but all finite numbers + 1 give the next finite number, and ω is DEFINED as the first transfinite ordinal, it can not exist.

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