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From: FromTheRafters <FTR@nomail.afraid.org>
Newsgroups: sci.math
Subject: Re: Does the number of nines increase?
Date: Tue, 16 Jul 2024 06:24:54 -0400
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Chris M. Thomasson pretended :
> On 7/15/2024 5:09 PM, Moebius wrote:
>> Am 16.07.2024 um 01:57 schrieb Moebius:
>> 
>>  > Siehe auch: https://en.wikipedia.org/wiki/Quantifier_shift
>> 
>> Hier wird als ein Beispiel für diesen Fehlschluss angeführt:
>> 
>> 3. Every natural number ? has a successor ? = ? + 1, the smallest of all 
>> natural numbers that are greater than ?. Therefore, there is a natural 
>> number ? that is a successor to all natural numbers.
>> 
>>      ∀? ∃? ??? ⊢ ∃? ∀? ???.
>> 
>> It is fallacious to conclude that there is a single natural number that is 
>> the successor of every natural number.
>
> There are infinite successors to any finite number?

'Infinitely many' would be a better way to state this.