Re: The set of necessary FISONs

On 07.02.2025 09:59, joes wrote:

N is exactly the set of all, and only the natural numbers.
It does not matter that you call it N_def.

It is described by the axioms 1 ∈ ℕ and n ∈ ℕ ==> n+1 ∈ ℕ. This is an infinite set containing all natnumbers.
The set M of all FISONs is described by the axioms F(1) ∈ M and F(n) ∈ M ==> F(n+1) ∈ M . This is an infinite set containing all FISONs.

Your extension of
that set is unclear, since you have not provided any axioms.

Cantor claims that *a fixed quantity greater than all natural numbers* exists.
An increasing sequence of natural numbers is never greater than all natural numbers.

If the set M is described as the smallest set satisfying F(1) ∈ M and
F(n) ∈ M ==> F(n+1) ∈ M then M contains all FISONs which can be
subtracted from U(Fn)) without changing the assumed result ℕ.

Wrong. M cannot be finite.

Inductive sets are infinite sets, according to set theory.
Regards, WM