On 2/16/2025 5:51 AM, WM wrote:
On 15.02.2025 20:41, Jim Burns wrote:
On 2/15/2025 7:56 AM, WM wrote:
On 14.02.2025 20:48, Jim Burns wrote:
swaps such that, after all swaps,
Bob is not anywhere he has swapped to.
>
Then your logic allows
lossless exchanges with losses.
Not acceptable.
>
If you accept ST+F
>
I don't.
Do you understand what an implication is?
If you accept ST+F, then
not.accepting the consequences of ST+F
is not an option.
Which parts of ST+F do you (WM) reject?
The key parts requiring,
after all swaps,
Bob not.being anywhere that he has swapped to
are
the empty set existing, and,
for existing X and y, adjunct X∪{y} existing.
Those seem unlikely candidates for rejection,
but you (WM) keep saying "set theory".
Perhaps I should take you at your word.
Do you (WM) reject set equality (extensionality)?
(Two sets with the same members are the same set.)
As it is with the existence or non.existence of ℕ
that is not as important as it looks at first.
A description of what would be in ℕ,
a description of a natural number,
does the work of ℕ,
but with more effort to describe and understand.
A description of being the same set
does the work of extensionality
but with more effort to describe and understand.
Everything about sets comes down to membership '∈'.
Two sets are the same set iff
they have the same members and also
they are members of the same sets.
There is nothing else left to reject in ST.
If you don't reject them, then what?
Do you reject the NONexistence of INFINITE sets?
That's what F claims.
It seems highly unlikely that you reject that.
What's left?
Increasingly fundamental, odd.if.rejected assumptions.
Do you reject that
a finite sequence of claims with no first false claim
has no false claim?
Then you (WM) don't know what 'finite' means.
Do you reject the NONexistence of
sets with sometimes.in sometimes.out members?
Then you (WM) don't know what 'set' means.
Everything points to you (WM) WANTING to
heckle actual mathematicians, except that
you (WM) haven't yet figured out
how to work the doorknob letting you into
the room where the discussion takes place.
https://en.wikipedia.org/wiki/Dunning%E2%80%93Kruger_effectIf you accept ST+F
>
I don't.
That probably should be treated the same as
your sitting on a park bench, and
telling the squirrels how brilliant you are.
The set of rows, the set of columns, and ⋃{F}
do not change.
>
Then it would need to contain ℕ,
as an infinite FISON.
>
Infinite FISONs
(finite initial segments of naturals)
are not acceptable.
>
Correct. Therefore the figure
{1}
{2, 1}
{3, 2, 1}
...
is finitely broad and finitely high.
No.
For each FISON, a broader, higher FISON exists.
For each FISON, the figure is not that broad or high.
The set of necessary FISONs
Re: The set of necessary FISONs