Re: The set of necessary FISONs

On 28.01.2025 18:18, FromTheRafters wrote:

WM expressed precisely :

On 28.01.2025 11:26, FromTheRafters wrote:

WM expressed precisely :

>

An infinite set of FISONs that has the union ℕ needs a first element.

>

The only needed one would be the last one but there is no last one just like there is no last natural number.

The only needed one would be a FISON that does not obey
|ℕ \ {1, 2, 3, ..., n}| = ℵo
but
|ℕ \ {1, 2, 3, ..., n}| = 0
But it is not existing. Therefore you claim that an infinite set is necessary. But that is pure matheology.
Assume any set of FISONs with uninon U(F(n)) = ℕ. Then every FISON can be dropped as completely useless. Nothing remains. Therefore:
IF U(F(n)) = ℕ THEN ℕ = { }.
FISONs can accomplish only a potentially infinite collection.
Regards, WM