Re: The set of necessary FISONs

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.

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.

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
For each set W which has, for each FISON F′,
a subset S′ ⊆ W larger than F′
W is not smaller than ⋃{F}
A subset is not larger than its superset.

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

For each FISON F′
there is a larger subset of rows
there is a larger subset of columns
The set of rows is not smaller than ⋃{F}
The set of columns is not smaller than ⋃{F}
The set of rows are subset ⋃{F}
The set of columns are subset ⋃{F}
The set of rows is not larger than ⋃{F}
The set of columns is not larger than ⋃{F}
The set of rows and the set of columns
are both the size of ⋃{F} and each other.