Re: The set of necessary FISONs

On 1/29/25 3:34 AM, WM wrote:

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

Which would mean the infinite set N has the same number of eleents as the Finite set of that FISON.

 But it is not existing. Therefore you claim that an infinite set is necessary. But that is pure matheology.

No, your logic is pure Naivity, by assuning the existance of non-existant sets.

 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 = { }.
 

Nope, Just shows your Naive Mathematics is based on Naive Logic that can't tell the difference between ANY and ALL.

FISONs can accomplish only a potentially infinite collection.

No, the COMPLETE set of FISONs are, and can accomplish the actual infinity.
All you are showing is that you logic can't even handle the potentially infinite, because it is based on naive assumptions that imply finiteness.

 Regards, WM
 

Sorry, all you are doing is proving your stupidity.