Re: Replacement of Cardinality

On 8/21/24 6:44 AM, 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. It exists at x > 0 because NUF(0) = 0.
 Regards, WM
 

But the other end doesn't "begin" with a first Natural Number Unit fraction, if it has a beginning that will be a trans-finite number.