Re: how

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

Le 22/06/2024 à 13:58, Jim Burns a écrit :

[...]

>
The set of FISONs has a smallest element, {1}.
>
The set of FISONs  covering the first 100 natnumbers
has a smallest element, namely {1, 2  3, ..., 100}.
>
The set of FISONs

The set of Finite.Initial.Segment.Of.Naturals

covering the natural numbers has no first element.
On the contrary we can prove that every FISON fails.
>
Only
a very fanatic matheologian like Franz Fritsche
can claim, that
the union of FISONs is infinitely larger than
every FISON [each FISON].

⋃{FISON} is an ISON, an Initial.Segment.Of.Naturals.
Each Finite.Initial.Segment.Of.Naturals ≠ ⋃{FISON}
Your (WM's) "argument" is that it is fanatic matheology
to claim that ⋃{FISON} is an IISON
an Infinite.Initial.Segment.Of.Naturals.
Other than proof.by.insult.comic.routine,
what have you (WM) got?

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

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

For what reason do we have that, other than
saying.otherwise is fanatic.matheology?
Do you (WM) have a math.like reason?