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NNTP-Posting-Date: Sat, 02 Nov 2024 22:08:18 +0000
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Newsgroups: sci.math
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From: Ross Finlayson <ross.a.finlayson@gmail.com>
Date: Sat, 2 Nov 2024 15:08:17 -0700
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On 11/02/2024 01:22 PM, Chris M. Thomasson wrote:
> On 11/2/2024 11:03 AM, Ross Finlayson wrote:
>> On 11/02/2024 06:54 AM, FromTheRafters wrote:
>>> WM was thinking very hard :
>>>> On 01.11.2024 22:53, FromTheRafters wrote:
>>>>> WM explained on 11/1/2024 :
>>>>>> On 01.11.2024 19:39, FromTheRafters wrote:
>>>>>>> WM formulated the question :
>>>>>>
>>>>>>>>> Infinite subsets don't do that for you, even if you wish really
>>>>>>>>> hard.
>>>>>>>>
>>>>>>>> They cannot evade if they are invariable.
>>>>>>>
>>>>>>> Sets don't change.
>>>>>>
>>>>>> Therefore the elements do not depend on us and our knowledge. "If I
>>>>>> find x, then I can find x + 1" is not relevant. "For every x (that I
>>>>>> find) there is x + 1" is no relevant. All elements are there,
>>>>>> independent of what we know or do. Therefore the first and the last
>>>>>> are also there independent of us. If they weren't, their existence
>>>>>> would depend on some circumstances and could change.
>>>>>
>>>>> Circumstances like "there is no last element"?
>>>>
>>>> That means, there is always another element. Potential infinity.
>>>
>>> Sets don't change. Forget about amplifying 'not finite' with such as
>>> 'actual' and potential' -- infinite simply means not finite and
>>> 'actual/potential' is a distinction without a difference. A useless
>>> concept outside of math philosophy.
>>>
>>>>> the set of denominators have no largest element to 'start' with.
>>>>
>>>> If all unit fractions are existing, then a smallest unit fraction is
>>>> existing. If NUF(x) has grown to ℵ₀ at x₀, then ℵ₀ unit fractions must
>>>> be between 0 and x₀. Hence at least ℵ₀ points with ℵ₀ intervals of
>>>> uncountably many points must be between 0 and x₀. That cannot happen
>>>> at x₀ = 0.
>>>>
>>>> Is that too hard to understand?
>>>
>>> Apparently, for you.
>>
>> Au contraire, there are multiple law(s) of large numbers,
>
> What about this sucker (42^999429994299942) * 2 ?
>
> Oh, don't forget about ((42^999429994299942) * 2) + 1   damn it!
>
>
>
>> and in mathematics like emergence after convergence,
>> the potential / practical / effective / actual distinction,
>> of "infinity", is a thing.
>>
>> You know who discovered mathematics? Philosophers.
>>
>>
>

Well, I frame it about Cantor space, because, there are
some facts deducible from the asymptotic density of zero's
and one's, in the rows and columns Cantor space, even if
there are infinitely or trans-finitely many.

For example, Borel and "combinatorics" disagree about how
many of the sequences are "absolutely normal" or "*-distributed",
almost all or almost none,
so there are at least two kinds, then there's also a third,
where about half of them are like so, "Square Cantor Space",
that there are three continuous domains, like line-reals field-reals
signal-reals, three perspectives of Cantor space Sparse Square Signal,
three limit theorems of probability Central Uniform Polar,
and otherwise at least three major criteria of convergence,
not necessarily agreeing, with regards to fast and slow,
and particularly the asymptotic freedom, where the limit
equals one, for example, yet "the infinite limit" equals zero.

Otherwise what you have there are arbitrarily large numbers,
finite though of course, instead we can use deduction to
reason about the really mathematical infinite, because the
plain old phenomenological results Sand-Reckoning.


It's usually or here it is attributed to Duns Scotus since
when "infinity is in: the numbers", then also associated
with Kant's Sublime, then it's for thinking beings to arrive
at that naive inference it is not, it is.