Re: how

On 5/6/24 4:20 PM, WM wrote:

Le 04/05/2024 à 05:18, Richard Damon a écrit :

On 5/3/24 9:21 AM, WM wrote:

 

Every findable number has ℵo successors. ==> Not all can be found.
All natural numbers have no successors. ==> There are more.

>
So, what is your actual definition of a "findable" number?

 A number that can be put in trichotomy with its neighbours.

>
How does that definition actually differ IN ITS DEFINITION from the definition of the Natural Numbers?

 The set of all natural numbers consists mainly of dark numbers. All numbers which can be put in trichotomy belong to a finite set
∀n ∈ ℕ_def: |ℕ \ {1, 2, 3, ..., n}| = ℵo
 which is followed by an infinite set the numbers of whch cannot be distinguished and which can only be manipulated collectively.
 |ℕ \ {1, 2, 3, ...}| = 0
 Regards, WM
 

Nope, and GIVEN Natural Number is followed by an infinte set of numbers above it, but ALL of those Natural Numbers meet your definition of "findable", as EVERY one of those numbers has a number before it and after it.
That this seems unbelievable just shows how little your comprehension understands how infinte sets can work.