Re: Contradiction of bijections as a measure for infinite sets

On 4/9/24 8:22 AM, WM wrote:

Le 09/04/2024 à 01:54, Jim Burns a écrit :

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=0 ∨ ∃⟦0,k⦆: ∀i ∈ ⟦0,k⦆: i⁺¹ ∈ ⦅0,k⟧

 Not correct if there are all natural numbers such that no further one exists below ω. Multiplication by 2 creates numbers beyond ω, or there would be numbers immune to multiplication.
 Regards, WM

Nope, because there isn't a "last" natural number, so the statement "no further one exists" isn't factual, but your false logic of using logic that only works on finite sets on an infinite set.
Multiplying ANY Natural numbers (which are all finite) by two, results in another finite Natural Number.