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NNTP-Posting-Date: Tue, 27 May 2025 20:38:12 +0000
Subject: Re: Log i = 0
Newsgroups: sci.math
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From: Ross Finlayson <ross.a.finlayson@gmail.com>
Date: Tue, 27 May 2025 13:38:19 -0700
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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.