Re: The set of necessary FISONs

On 13.02.2025 20:47, Jim Burns wrote:

On 2/13/2025 7:04 AM, WM wrote:

On 13.02.2025 00:49, Jim Burns wrote:

 

Learn that
by A(1) and if A(n) then A(n+1)
an infinite set is created

 described
 

which has no successors.

 Each FISON has a successor in the set of FISONs.
The set of FISONs isn't any FISON.

The set of all FISONs is created.

 

Learn that if there were successors,
they would have a fixed first element.

 Since induction on the set of FISONs concerns
a predicate on FISONs, not the set of FISONs,
presence or absence of successors for
the set of FISONS and anything else not.in
the set of FISONs
is irrelevant.

No, induction concerns alle the natural numbers n of the FISONs A(n).

 

Learn that
{1}
{2, 1}
{3, 2, 1}
...
is not longer than broad.

 For each set A which has
emptier.by.one subsets A\{a} smaller than A
there is a FISON larger than A

Irrelevant. All are finite and will never become infinite.

The set of rows and the set of columns
are both the size of ⋃{F} and each other.
 

Yes, that is potentially infinite.
Regards, WM