Re: Replacement of Cardinality

On 2024-08-21 12:24:14 +0000, WM said:

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.

 

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

 

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

Seems that you are making hidden assumptions about the end of endless.
--
Mikko