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NNTP-Posting-Date: Fri, 19 Jul 2024 02:37:19 +0000
Subject: Re: More complex numbers than reals? (complex)
Newsgroups: sci.math
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From: Ross Finlayson <ross.a.finlayson@gmail.com>
Date: Thu, 18 Jul 2024 19:37:15 -0700
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On 07/18/2024 02:51 PM, Jim Burns wrote:
> On 7/18/2024 4:50 PM, WM wrote:
>> Le 18/07/2024 à 20:49, Jim Burns a écrit :
>
>>> ℵ₀.many remain in E(n)
>>> 0.many remain in all.infinite (all) end segments
>>
>> Each infinite endsegment has infinitely many numbers.
>> How many are not in all predecessors?
>
> You are confused about
> the intersection of all end segments.
>
> Each infinite end.segment has infinitely many numbers.
> Each is not in all.infinite (all) end segments.
>
> It is insufficient to be in all _predecessor_ end.segments.
>
>

Yet, there's a case for induction
that there's no case for induction,
which axiomless deduction usually
arrives at as insufficient.

Maybe it helps to think of the numbers
as ranging from zero to a large number,
then that it's infinite in the middle.


How about if there are _less_ complex numbers
than reals? Sort of like the cardinal 1 in
set theory is the equivalence class of all
singletons, that instead of the integers being
defined first, instead it's just that there
the modular, regular culminations,
regular in density, regular in dispersion,
and otherwise reflecting that multiple rulialities,
multiple regularities, must be resolved by deduction,
that otherwise just makes an inductive impasse
both ways, between points and lines and lines and points.

Just "axiomatizing" least-upper-bound of point-sets
as modeling geometry's given lines, some have as,
"insufficient". (Not "true".)

Mathematics: there is one.