Re: Replacement of Cardinality

On 8/28/2024 12:13 AM, Jim Burns wrote:

On 8/27/2024 3:11 PM, WM wrote:

Le 27/08/2024 à 02:06, Jim Burns a écrit :

On 8/25/2024 3:45 PM, WM wrote:

This function exists because
nothing contradicts its existence.

Except for the contradicting
consequences of its existence.

The function exists if
actual infinity exists.
The function does not exist if
only potential infinity exists.

¬∃ᴿx>0: NUF(x) = 1

Then NUF(x) does not exist
and infinity is not actual
and sets are not complete.

In a finiteⁿᵒᵗᐧᵂᴹ order ⟨B,<⟩
each non.empty S ⊆ B is 2.ended.

In a finiteᵂᴹ order ⟨B,<⟩
no one can say
what a setᵂᴹ is,
what an orderᵂᴹ is,
what finiteᵂᴹ is.
Perhaps, in 30 more years,
these question will have answers.

An infiniteⁿᵒᵗᐧᵂᴹ order ⟨B,◁⟩ is
trichotomous and not finiteⁿᵒᵗᐧᵂᴹ.

Trichotomous? Did you actually mean to say "dense order", "dense in
itself", or something else akin?

<SNIPPING>
--
Jeff Barnett