Re: Contradiction of bijections as a measure for infinite sets

On 4/8/2024 10:48 PM, Moebius wrote:

Am 09.04.2024 um 03:54 schrieb Jim Burns:

On 4/8/2024 9:55 AM, WM wrote:

Le 07/04/2024 à 21:47, Jim Burns a écrit :

The successor operation is closed in
the natural numbers.

>
For visible numbers only.

>
Visibleᵂᴹ or darkᵂᴹ,
k is a natural number  :⟺

>
k e IN.
(I hope that you don't mind
that slight simplification).

I welcome your comment,
as a change of pace,
even if there were no other reason.
The reason I wrote things out this way

k=0 ∨ ∃⟦0,k⦆: ∀i ∈ ⟦0,k⦆: i⁺¹ ∈ ⦅0,k⟧

is that I want to express "natural number"
without depending upon "what everyone's saying"
A large part of the struggle going on here
isn't really over mathematics at all.
Instead, it is over _what are we talking about_
Here, with WM,
depending upon "what everyone's saying"
is a certain path to WM taking what I'm saying
some other way. That becomes more difficult, at least,
if I embed _the way to take what I'm saying_
over and over and over.