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From: Python <python@invalid.org>
Newsgroups: sci.logic,sci.math
Subject: Re: Replacement of Cardinality (defining numbers as half finite, half
 infinite)
Date: Tue, 13 Aug 2024 05:10:44 +0200
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Le 13/08/2024 à 05:07, Ross Finlayson a écrit :
> On 08/06/2024 07:30 PM, Ross Finlayson wrote:
>> On 08/06/2024 05:37 PM, Moebius wrote:
>>> Am 07.08.2024 um 02:27 schrieb Jim Burns:
>>>
>>>> however things stand with supertasks, [...]
>>>
>>> Here my 2 cents: Some "supertasks" (thought experiment) DO lead*) to a
>>> specific "final result" (from a "logical" point of view), some NOT.
>>>
>>> Thomson's Lamp is of the latter type.
>>>
>>> It's final state is simply not "determined" by all it's "earlier" 
>>> states.
>>>
>>> _____________________
>>>
>>> *) in a certain sense; usually considering some additional assumptions.
>>
>> In nature, in the very heart of the nucleus of the atom,
>> where according to plain mathematics the most concentrated
>> force of the strong nuclear force that holds the atom's
>> nucleus together would be, is: "asymptotic freedom".
>>
>> As a supertask, according to induction, in the concentric
>> model of the force that is the binding energy that holds
>> together the very substance of matter itself, in the theory,
>> is "asymptotic freedom".
>>
>> This is as was theorized by Salam and Weinberg in the 1970's,
>> and within a few years for which prizes in physics were awarded.
>>
>> The geometric series, Zeno's, adds up to one. Of course, in
>> nature, in the mesoscale or the classical, that's always
>> perfectly true.
>>
>>
>> The idea that there are anti-inductive results in the
>> infinitary, is even a bit stronger than the usual apeiron
>> or non-results in the infinitary, though, the most usual
>> combined inductive and deductive results, about the
>> infinitely-divisible in a space, are most strong.
>>
>> That is to say, calculus is imperfect and only at best
>> a close approximation and always with a non-zero error term,
>> except in the infinite limit, where it is perfect, and,
>> it not only goes to that once, it must be that it goes to
>> that all the many times, because we don't merely have a
>> fundamental theorem of differentiation, yet a fundamental
>> theorem of integration, which sums no less than infinitely
>> many areas to be correct in the usual sense, and no less.
>>
>>
>> These days some peopls don't even know that various
>> conjectures of Goldbach in the number-theoretic, or
>> about the lengths of arithmetic progressions or Szemeredi,
>> are rather formally undecide-able and with models of
>> standard and non-standard integers, both fragments
>> and extensions, both so and not so.
>>
>>
>> Then, induction, alone, does not suffice, and,
>> deduction, together with properties of the space
>> like constancy in measure and proportion in relation,
>> make so that the geometric series has a sum.
>>
>> Calculus is only correct in the _infinite_ limit.
>>
>>
>> Then, for mathematical platonists, that must be real
>> somehow, just like there's no perfect circle, yet there
>> is, an object of mathematics, there's infinity,
>> an object of mathematics.
>>
>>
>> Then, results in the non-standard like summing the
>> geometric series or Zeno's, or everyone's favorite
>> first non-standard not-a-real-function Dirac's delta,
>> which you can notice on the Wiki is called a "function",
>> again, continue.
>>
>>
> 

Ross, could you reach friends? Family? Any kind of social
service professionals? Neighborhoods? Whatever. You are not
going well AT ALL.