Re: Replacement of Cardinality (ubiquitous ordinals, integer continuum, linear continuum, continuity)

On 01/01/2025 01:14 PM, Jim Burns wrote:

On 1/1/2025 1:10 PM, Ross Finlayson wrote:

On 07/29/2024 12:46 PM, Ross Finlayson wrote:

On 07/29/2024 12:44 PM, Ross Finlayson wrote:

On 07/29/2024 05:32 AM, Jim Burns wrote:

On 7/28/2024 7:42 PM, Ross Finlayson wrote:

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about ubiquitous ordinals

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What are ubiquitous ordinal?

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The "ubiquitous ordinals", sort of recalls Kronecker's
"G-d made the integers, the rest is the work of Man",

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I think Kronecker's integers are the finite ordinals.
Are you saying that 'ubiquitous' means 'finite'?
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So, "ubiquitous ordinals" is exactly what it says.

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It's surprising how unhelpful some answers can be.
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Or, you know, "infinity plus one".

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Consider the definition of a finite.cardinal as
the cardinal #A of a set A
smaller.by.one than sets fuller.by.one
#A ∈ ⟦0,ℵ₀⦆  :⇔  (#A < #(A∪{a}) ⇐ A ≠ A∪{a})
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If,
as might be expected,
infinity.plus.one is different from simple.infinity,
then,
under that definition,
infinity is finite.
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It's "well-ordering the universe".
Yeah, I know, you don't have a universe in your theory,
as you say that there's no meta-theory your theory,
yet, what's that then, all one theory?
So, I imagine it's sort of like "Cohen's M's", M for model.
Well good luck then, this is one of the examples of
the many, many trails with novel sorts content that
are quite altogether different from the many, many
circles of the usual tit-for-tat-trolls.
It's like compression, and signal to noise, that
when all the Dumb-Em posts can be compressed to
about zero, or, just a starter for establishing
contradistinctory duals, here it's that there is
at least one signal for all our noise.
Warm regards then