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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.logic,sci.math
Subject: Re: Replacement of Cardinality
Date: Tue, 27 Aug 2024 22:16:16 -0400
Organization: i2pn2 (i2pn.org)
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On 8/27/24 3:57 PM, WM wrote:
> Le 27/08/2024 à 21:31, Moebius a écrit :
>>>>> On 8/25/2024 3:45 PM, WM wrote:
>>>>
>>>>>> This function exists because
>>>>>> nothing contradicts its existence.
>>
>> Right. But the values of the function NUF are:
>>
>> 0 for all real arguments <= 0 and aleph_0 for all real arguments > 0.
> 
> Correction: For all ends of real intervals containing ℵo unit fractions. 
> The interval (0, x) cannot contain ℵo unit fractions unless x is 
> sufficiently large.
> 
> Regards, WM

But sufficiently large is just being any finite positive number.

Then it contains the Aleph_0 unit fractions starting at 1/ceil(1/x)

Since it is a fact that for ANY Natural Number n, there are aleph_0 
other Natural Numbers after it, since aleph_0 is not exhausted by trying 
to reduce it by finite amounts.