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From: Moebius <invalid@example.invalid>
Newsgroups: sci.logic,sci.math
Subject: Re: Replacement of Cardinality
Date: Mon, 5 Aug 2024 01:12:21 +0200
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Am 04.08.2024 um 22:16 schrieb Jim Burns:
 > On 8/4/2024 2:13 PM, WM wrote:

 >> When all x are involved,
 >> the universal quantifier is usually not written.

 > When a universal quantifier is not written,
 > it is implicit, and
 > it can only stand implicitly outside the formula.

Right. Still there's a distinct problem with "implicit quantification" 
IN THIS CASE. (Hence WM's "argument" is nonsense anyway.)

Here we need "∀x > 0". Clearly an "implicit quantifier" does not know 
that he's restricted to "x > 0".