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From: Moebius <invalid@example.invalid>
Newsgroups: sci.logic,sci.math
Subject: Re: Replacement of Cardinality
Date: Fri, 2 Aug 2024 19:08:07 +0200
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Am 02.08.2024 um 18:35 schrieb Jim Burns:
> On 8/2/2024 7:40 AM, WM wrote:
>> Le 01/08/2024 à 18:43, Jim Burns a écrit :
>>> On 8/1/2024 8:02 AM, WM wrote:
> 
>>>>>> ∀n ∈ ℕ: 1/n - 1/(n+1) > 0.
>>>>>> Note the universal quantifier. 
> 
>>>> It is not a contradiction to my formula
>>>> if some n has no n+1.
>>>
>>> No, it literally contradicts your formula
>>> for some n e N to not.have n+1
>>
>> My formula is explicitly valid only for natural numbers.

This is one of Mückenheim's brainfarts.

I guess what he means is:

     "1/n - 1/(n+1) > 0" is (especially) valid for (all) natural numbers n ,

or something like that.

To state that a closed formula / sentence / statement "is valid ... for 
natural numbers" is just mumbo-jumbo.