Re: Replacement of Cardinality (roots of zero, reciprocals of the multiplicative annihilator)

On 08/23/2024 09:30 PM, Jim Burns wrote:

On 8/23/2024 8:05 PM, Moebius wrote:

Am 24.08.2024 um 00:04 schrieb Jim Burns:

>

x = 1/0  :⇔  0⋅x = 1
¬∃x ∈ R: x = 1/0

>
Nonsense.

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| 1.3 Stipulative definitions
|
| A stipulative definition imparts a meaning to the defined term,
| and involves no commitment that
| the assigned meaning agrees with prior uses (if any) of the term.
| Stipulative definitions are epistemologically special.
| They yield judgments with epistemological characteristics that
| are puzzling elsewhere.
| If one stipulatively defines a “raimex” as, say,
| a rational, imaginative, experiencing being
| then the judgment “raimexes are rational” is assured of
| being necessary, certain, and a priori.
>
|  See Frege 1914 for a defense of the austere view that,
| in mathematics at least,
| only stipulative definitions should be countenanced.
>
| Frege, G., 1914, “Logic in Mathematics,”
| in _Gottlob Frege: Posthumous Writings_
| edited by H. Hermes, F. Kambartel, and F. Kaulbach,
| Chicago: University of Chicago Press (1979), pp. 203–250.
>
https://plato.stanford.edu/entries/definitions/
>
Stipulate.
x = 1/0  :⇔  0⋅x = 1
>
Lemma.
¬∃x ∈ R: x = 1/0
>
>

You mean zero's the multiplicative annihilator and
that it's the only value in the field that carries
operands to a non-unique result among otherwise
the pair-wise combinations of the operands?
That the reciprocal of a multiplicative annihilator
introduces a description of a multiplicative annihilator
and as well a multiplicity of "roots of zero"?
Let's see, while you guys start straw-man soft-balling
each other, about division by zero being undefined,
some people already know that the regular singular points
of the hypergeometric are already given as 0, 1, and infinity.
How about, in the context of all the many grains
of sand on all the beaches of the world, just a
truckload of sand. You going to count those, too?
Anyways it's already given that the regular singular
points of the hypergeometric are "0, 1, infinity".