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From: joes <noreply@example.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Date: Sat, 2 Nov 2024 12:11:08 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Sat, 02 Nov 2024 10:59:04 +0100 schrieb WM:
> 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.
Independently nonexistent.

>>> 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.
No, it's just a property of the infinite, especially the actual.

>> the set of denominators have no largest element to 'start' with.
> If all unit fractions are existing, then a smallest unit fraction is
> existing.
Invalid deduction.

> 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.
Well AT zero the value is 0. No UF is zero or less...

-- 
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.