Re: Replacement of Cardinality (book-keeping sign)

On 08/27/2024 04:06 PM, FromTheRafters wrote:

WM wrote :

Le 25/08/2024 à 23:18, Jim Burns a écrit :
>

Therefore,
there is no ω-1,

>
If the set of ordinal numbers is complete, then ω-1 precedes ω - by
definition.

>
What is the definition of subtraction here? Can you subtract past zero
in the naturals?

You can build a little mound out past ten, say,
then relate that to zero in a sliding scale,
then if you find you can't remember how to roll the clock back,
you can count so many forward howsoever many were lost,
with a bit of book-keeping then it so results,
that the extra cost involved in counting over numbering,
lets you build the integers as deep as they are.