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From: Moebius <invalid@example.invalid>
Newsgroups: sci.math
Subject: Re: Replacement of Cardinality
Date: Sun, 4 Aug 2024 20:12:19 +0200
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Am 04.08.2024 um 19:59 schrieb Jim Burns:
> On 8/4/2024 11:44 AM, WM wrote:
>> Le 03/08/2024 à 19:42, joes a écrit :
> 
>>> [...]
>>
>> The reversed quantification is nonsense
> 
> ...because from ∀x∃u to ∃u∀x is unreliable.
> 
>  From ∃u∀x to ∀x∃u  is reliable.
>  From ∃u∃x to ∃x∃u  is reliable.
>  From ∀u∀x to ∀x∀u  is reliable.
> However,
> from ∀x∃u to ∃u∀x is unreliable.
> 
> In some cases,
> from ∀x∃u to ∃u∀x is not.only.unreliable,
> it is incorrect.

Example (referring to FOPL= only):

     ∀x∃u x = u     (true)

     ∃u∀x x = u     (false)

for any universe of discourse with more than one "entity" (object).