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From: joes <noreply@example.org>
Newsgroups: sci.math
Subject: Re: quantifier shift
Date: Sat, 5 Oct 2024 13:00:22 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Sat, 05 Oct 2024 11:43:50 +0200 schrieb WM:
> On 05.10.2024 10:46, Moebius wrote:
> 
>> a quantifier shift is NOT reliable und wird daher in der Mathematik
>> tunlichst vermieden (und nicht nur dort).
> I many cases it is correct. For instance if every definable natural
> number has ℵo natural successors, then there are ℵo natural numbers
> larger than all definable natural numbers. They are dark however and
> cannot be specified.
Since it is logically invalid, you need to prove your deduction
independently. In general those are two different propositions.

-- 
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.