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From: Tom Bola <Tom@bolamail.etc>
Newsgroups: sci.math
Subject: Re: because =?utf-8?Q?g=E2=A4=A8(g=E2=81=BB=C2=B9(x))?= = g(y) [1/2] Re: how
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Am 01.05.2024 23:46:38 Moebius schrieb:

> Am 30.04.2024 um 15:12 schrieb WM:
> 
>>> If n is before ω then n⋅2 is before ω. (*) 
>> 
>> That is not true.
> 
> Doch, doch, Mückenheim, das ist wahr.
> 
> Für den Beweis brauchen wir lediglich 2 (im Rahmen der ML beweisbare) 
> Tatsachen:
> 
> (1) n < ω <-> n e IN
> 
> und
> 
> (2) An e IN: n⋅2 e IN ,
> 
> sowie die Definition:
> 
> (3) x is /before/ y iff x < y.
> 
> Nun der Beweis von (*):
> 
> Es gelte "n is before ω", d. h. mit (3): n < ω. Mit (1) folgt daraus n e 
> IN und daher mit (2) n⋅2 e IN. Mit (1) folgt daraus n⋅2 < ω und mit (3) 
> dann "n⋅2 is before ω". Wir haben mithin also gezeigt, dass "If n is 
> before ω then n⋅2 is before ω" gilt. qed

passt... (oder auf 'nntp': ack)