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From: "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Date: Sat, 2 Nov 2024 13:22:19 -0700
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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.
> 
>