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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions?
Date: Sat, 5 Oct 2024 07:14:16 -0400
Organization: i2pn2 (i2pn.org)
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On 10/5/24 5:43 AM, WM wrote:
> 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.
> 
> Regards, WM
> 

But they are not dark, but can be specified.

Just because they were bigger than one arbitrary number you chose, 
doesn't mean you can't choose one bigger.

The problem is there is not a biggest number you can choose, like you 
want to assume, and that blows up your logic to smithereens.