Re: Log i = 0

On 06/06/2025 06:03 AM, Julio Di Egidio wrote:

On 30/05/2025 02:11, Ross Finlayson wrote:

On 05/29/2025 11:25 AM, WM wrote:

On 29.05.2025 17:37, Ross Finlayson wrote:

<snip>

It seems you're describing a simple book-keeping of an integer
continuum
in areal terms.
>
Also called a geometrization sometimes.

>
Right. Do you understand the result?

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You can build it in Katz' OUTPACING simply enough,
that more is larger.
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That depends on a particular structure though, like geometry,
or often enough the integer lattice.
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Then that something is recursively self-similar, like the
"infinite balanced binary tree", any node of which is a copy
of the root, or "square Cantor space" where all the sequences
of 0's and 1's are in lexicographic order in the language of 2^w,
that's mostly defined by square Cantor space being an arithmetization
of a geometrization of a line-drawing the interval [0,1].
>
The only way I'd suggest you're making sense at all is to
agree with everything I say, and retroactively.

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Yep, except that "Cantor" arithmetizes [0,1] into [0,1).
>
-Julio
>

Yet, arithmetization is a mere attempt of geometrization,
or that's sort of what I've been reading from Struick,
where Struick's "History of Mathematics" is pretty great,
as with regards to Poncelet to Poincare, that arithmetization
is a great sort of digital effort, yet a continuum mechanics
has a real geometry, so Kronecker-type arithmetizations and
algebraizations may only attain to geometrization, then that
the inductive impasses of arithmetization and algebraization
their completions (like, point-sets to a line): yet belong
more to Vitali and Hausdorff than Banach and Tarski.
It's like Lefschetz says, "we're algebraic GEOMETERS".
Anyways the n/d bit or "natural/unit equivalency function"
or "equipollency function" if you'd rather, is quite plain
dirt simple, and then having simply worked up that besides
that via inspection it falls out of uncountability, then
that also Russell's axiom "not my paradox" gets disqualified,
and there's the extra-ordinary, then a ubiquitous ordinals,
for example as after axiomatized by Cohen at the end of
forcing, makes at least a paradox-free logical theory
with at least three models of continuous domains, only
one of which is Dedekind's and by that I mean Eudoxus',
the others called "Aristotle's" and "Nyquist and Shannon's".
Anyways there are plentiful multiplicities in "complex number
theory" yet there's more going on in the _original_ and about
the _original analysis_ of an identity dimension, that
if the complex numbers swirl around outside, say, it's the in-side.