Re: Replacement of Cardinality

Le 28/07/2024 à 20:17, Jim Burns a écrit :

On 7/28/2024 8:17 AM, WM wrote:

Le 27/07/2024 à 19:34, Jim Burns a écrit :

On 7/26/2024 12:31 PM, WM wrote:

 

_The rule of subset_ proves that
every proper subset has less elements than its superset.

 

If ℕ has fewer elements than ℕ∪{ℕ}
then
|ℕ| ∈ ℕ

>
|ℕ| = ω-1 ∈ ℕ

 No finite.ordinal is last.finite,
no visibleᵂᴹ finite.ordinal,
no darkᵂᴹ finite.ordinal.
In particular, no finite.ordinal is ω-1

NUF(x) cannot grow by more than 1 at any x. Therefore there is a first step. First unit fraction implies last natural number.

Also, no before.first infinite.ordinal is
before the first infinite.ordinal ω
In particular, no infinite.ordinal is ω-1

Don't claim. Explain how you imagine the positions of the unit fractions such that NUF does not have a first step.
Regards, WM