Re: Replacement of Cardinality

Am 30.08.2024 um 17:15 schrieb joes:

Am Fri, 30 Aug 2024 13:08:14 +0000 schrieb WM:

0 is below the end. Hence there is an end.

Does not follow.

Actually, it does!
If we have
       0 < the_smallest_unit_fraction (WM: "the end")
we may derive (in the context of FOPL)
       Ex(x = the_smallest_unit_fraction & 0 < x)
and from this:
       Ex(x = the_smallest_unit_fraction)
       "the_smallest_unit_fraction exists"
And from this "of course" we get: there is a
smallest unit fraction. (WM: "there is an end") :-P
On the other hand, (actually) the term "the_smallest_unit_fraction" (with the intended meaning) cannot be defined (i.e. introduced by a proper definition), since there is no smallest unit fraction.

Logic that depends on the existance of something that doesn't exist is
just broken.

Yeah. At least in the context of classical logic.