Re: how

Le 22/06/2024 à 20:20, Jim Burns a écrit :

On 6/22/2024 12:31 PM, WM wrote:

Your (WM's) "argument" is that it is fanatic matheology
to claim that ⋃{FISON} is an IISON
an Infinite.Initial.Segment.Of.Naturals.

That is impossible because all FISONs are finite.

According to Cantor's theorem B
a set of necessary FISONs to be unioned does not exist.

 According to proposal 3 == "∅, x∪{y}, {y:P(x)} exist"
a set of FISONS.to.be.unioned exists

A set of necessary FISONs to be unioned as ℕ does not exist.

 Removing a single FISON not.changes the union.
Removing all FISONs is not removing a single FISON
and changes the union.

What FISON is the first that must not be removed?

 

Therefore we have: UF(n) = ℕ ⟹ U{ } = ℕ.

 Do you (WM) have a math.like reason?

You are unfortunately unable to comprehend what you dislike: It is Cantor's Theorem B: Every existing set of ordinals has a first or smallest element. The set of FISONs necessary to yield ℕ would be a set of ordinals. It is well defined. For every FISON we can determine whether it is necessary.
Regards, WM