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Subject: Re: Incompleteness of Cantor's enumeration of the rational numbers
 (research)
Newsgroups: sci.math
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From: Ross Finlayson <ross.a.finlayson@gmail.com>
Date: Fri, 15 Nov 2024 09:44:08 -0800
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On 11/14/2024 06:22 PM, Ross Finlayson wrote:
> On 11/13/2024 06:04 PM, Ross Finlayson wrote:
>> On 11/13/2024 05:43 PM, Jim Burns wrote:
>>> On 11/13/2024 7:05 PM, FromTheRafters wrote:
>>>> Jim Burns formulated on Wednesday :
>>>>> On 11/13/2024 4:29 PM, WM wrote:
>>>>>> On 13.11.2024 20:38, Jim Burns wrote:
>>>
>>>>>>> ----
>>>>>>>>  Bob.
>>>>>>>
>>>>>>> KING BOB!
>>>>>>> https://www.youtube.com/watch?v=TjAg-8qqR3g
>>>>>>>
>>>>>>> If,
>>>>>>>   in a set A which
>>>>>>>   can match one of its proper subsets B,
>>>>>>
>>>>>> That is nonsense too.
>>>
>>> [repaired]
>>>
>>> A finite sequence of claims in which
>>> each claim is true.or.not.first.false
>>> is
>>> a finite sequence of claims in which
>>> each claim is true.
>>>
>>> Some claims are true and we know it
>>> because
>>> they claim that
>>> when we say this, we mean that,
>>> and we, conscious of our own minds, know that
>>> when we say this, we mean that.
>>>
>>> Some claims are not.first.false and we know it
>>> because
>>> we can see that
>>> no assignment of truth.values exists
>>> in which they are first.false.
>>> q is not first.false in ⟨ p p⇒q q ⟩.
>>>
>>> Some finite sequences of claims are
>>> each true.or.not.first.false
>>> and we know it.
>>>
>>> When we know that,
>>> we know each claim is true.
>>>
>>> We know each claim is true, even if
>>> it is a claim physically impossible to check,
>>> like it would be physically impossible
>>> to check each one of infinitely.many.
>>>
>>> We know because
>>> it's not checking the individuals
>>> by which we know.
>>> It's a certain sequence of claims existing
>>> by which we know.
>>>
>>>> In my source window:
>>>
>>> [...]
>>>>> That is nonsense too.
>>>>
>>>> A finite 𝘀𝗲𝗾𝘂𝗲𝗻𝗰𝗲 of 𝗰𝗹𝗮𝗶𝗺𝘀
>>>> in which
>>>> each claim is true.or.not.first.false
>>>> is
>>>> a finite 𝘀𝗲𝗾𝘂𝗲𝗻𝗰𝗲 of 𝗰𝗹𝗮𝗶𝗺𝘀
>>>> in which
>>>> each claim is true.
>>> [...]
>>>
>>>> ================================================
>>>> I follow some of this mostly from context. :)
>>>
>>> Sorry about that.
>>> The other fonts weren't strictly necessary,
>>> I just had a brainstorm over
>>> how to (maybe) explain logical validity better,
>>> and I couldn't resist.
>>>
>>>
>>
>> Some usual laws, or criteria, rather, of convergence,
>> fail, for example Stirling's formula.
>>
>> When are they ever wrong? Are there simply more
>> than a usual naive law of large numbers what's
>> merely the law of small numbers?
>>
>> Then, asymptotic freedom, or the Arago spot, make
>> examples of what do not arrive from inductive inference.
>>
>> So, these super-classical concerns are a thing.
>>
>> There's one rhyme,
>> "I like traffic lights,
>> I like traffic lights,
>> I like traffic lights, ...."
>>
>> Also usually called slippery slope,
>> shifting sands, or ad absurdam.
>>
>> Usually of course arrived at ultimately.untrue
>> from more objective concerns.
>>
>> Take a look to Chrysippus, he establishes great
>> grounds for modal (mood-al) logic and relevance logic about
>> hundreds of years before Plotinus arrived at
>> the "material inductive implication" the "quasi-modal",
>> and provides reasoning for more thorough accounts
>> when people might not have time to read and follow
>> both Aristotle's Prior, and Posterior sur-rounds
>> of inference.
>>
>> Or, "not.first.false" must yet also be "not.ultimately.untrue",
>> when _all_ the cases are run out.
>>
>> (Or, maybe it's the other way, ....)
>>
>> As long as you might agree that _all_ your stipulations be
>> read off in any order, that might help, it's a usual
>> criterion of constructivism.
>>
>> For structuralists and not merely the shallow feels.
>>
>>
>
>
> A finitary Kronecker's lemma and large deviations in the Strong Law of
> Large numbers on Banach spaces
>
> Duality on symmetric multiple polylogarithms
>
> Continuity of matings of Kleinian groups and polynomials
>
> Complexity of Finite Borel Asymptotic Dimension
>
> On limiting distributions of arithmetic functions
>
> Products of pseudofinite structures
>
> Spectral equivalence of nearby Lagrangians
>
> Sparser Abelian High Dimensional Expanders
>
> Probability Laws Concerning Zeta Integrals
>
>
> -- https://www.arxiv.org/list/math/recent
>
> Unified analysis of non-Markovian open quantum systems in Gaussian
> environment using superoperator formalism
>
> A generalization of the martingale property of entropy production in
> stochastic systems
>
> Superintegrability and Coulomb-Oscillator Duality
>
> Central limit theorem for the focusing Φ4-measure in the infinite volume
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