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From: Richard Damon <richard@damon-family.org>
Newsgroups: sci.math
Subject: Re: How many different unit fractions are lessorequal than all unit
 fractions? (infinitary)
Date: Thu, 31 Oct 2024 19:43:33 -0400
Organization: i2pn2 (i2pn.org)
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On 10/31/24 1:35 PM, WM wrote:
> On 31.10.2024 12:36, Richard Damon wrote:
>> On 10/30/24 11:38 AM, WM wrote:
> 
>>>> NUF(x) MUST jump from 0 to Aleph_0 at all real values x, as below 
>>>> ANY real number x, there are Aleph_0 unit fractions.
> 
> You cannot distinguish them by any real number? That proves that they 
> are dark.
> 
> Regards, WM
> 

They are not finite values.

We have gone over this before, and you keep on changing your mind, as 
you are stuck in an inconsistancy.

If you want a value where NUF(x) would be 1, it can not be in any of the 
finite number systems, as all of them have no smallest value.

They CAN be in a trans-finite number system, like the infinitesimals, 
but then they are not "dark", just non-finite.

When this is pointed out, you try to say that you mean for your dark 
numbers to be finite, but they can't be, as all those values are 
definable by the rules of the finite numbers.