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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: How many ... (Sparse, Signal, Square Cantor "SPACE")
Date: Sun, 3 Nov 2024 14:53:23 -0800
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On 11/3/2024 9:09 AM, Ross Finlayson wrote:
> On 11/02/2024 08:41 PM, Chris M. Thomasson wrote:
>> On 11/2/2024 3:08 PM, Ross Finlayson wrote:
>>> 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.
>> [...]
>>
>> Cantor Pairing is fun. Mapping to and fro. Nothing is lost. WM disagrees
>> here, but shit happens.
>>
>>
>>>
>>
> 
> Here's a way to think about it.
[...]

Cantor pairing works, and nothing is lost. That's that.