Re: Replacement of Cardinality

Am Wed, 21 Aug 2024 12:24:14 +0000 schrieb WM:

Le 21/08/2024 à 12:58, FromTheRafters a écrit :

WM wrote :

Le 20/08/2024 à 23:25, FromTheRafters a écrit :

WM explained :

Le 20/08/2024 à 12:31, FromTheRafters a écrit :

on 8/19/2024, Richard Damon supposed :

>

You can not derive a first number > 0 in any of the Number System
that we have been talking about, Unit Fractions, Rationals or
Reals, so you can't claim it to exist.

 
Not in their natural ordering.

>
Dark numbers have no discernible order. It is impossible to find the
smallest unit fraction or the next one or the next one. It is only
possible to prove that NUF(x) grows by 1 at every unit fraction. It
starts from 0.

>

Normally, the unit fractions are listed in the sequence one over one,
one over two, one over three etcetera. There is a first but no last.
Now you have started from the wrong 'end'

>
No, I have started from the other end.

Correct, that is the wrong end.

It is an end which proves dark numbers.

Why should there be an end in the first place? Are there not infinitely
many unit fractions?

It exists at x > 0 because NUF(0) = 0.

Since no unit fraction is below or at zero, the end is before. What
else?

--
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.