Re: Log i = 0

On 05/27/2025 09:05 AM, FromTheRafters wrote:

WM wrote :

On 26.05.2025 22:25, efji wrote:

Le 26/05/2025 à 16:36, WM a écrit :

That is wrong. Present mathematics simply assumes that all natural
numbers can be used for counting. But that is wrong.

>
What's the point ?
It is the DEFINITION of "counting". A countable infinite set IS a set
equipped with a bijection onto \N.
>

This bijection does not exist because most natural numbers cannot be
distinguished as a simple argument shows.

>
Bijected elements need not be distinguished, it is enough to show a
bijection.

Hmm, yes and no, there's Cantor-Schroeder-Bernstein establishing that
cardinality is a transitive property or comprises an equivalence class,
yet, that's for Cartesian functions, and some functions are not
Cartesian, where they are simply enough subsets of a Cartesian product
of two domains, the model of their elements.
So, in that sense those elements are distinct, for example line-reals'
countable continuous domain and field-reals' uncountable continuous
domain, that there isn't a non-Cartesian function between those two.
The usual yammer about the inductive set not being complete is
about the most usual thing, saying that Russell's retro-thesis
defined it away, doesn't really.
Zeroes are kind of like infinities (excuse if I confuse "zeros"
and "zeroes" with regards to plurals and a verb), they're singular
points of sorts, like the regular singular points of the hypergeometric
are zero, one, and infinity. So, there are all the non-principal
branches of what are otherwise distinctness results among what in
the branchless are uniqueness results.