Re: The set of necessary FISONs

On 10.03.2025 00:11, Jim Burns wrote:

On 3/9/2025 3:13 PM, WM wrote:

You even avoid hearing what we mean.

>
I am interested in
the difference
that you see between
>
Z₀ defined by { } ∈ Z₀, and
if {{{...{{{ }}}...}}} with n curly brackets ∈ Z₀
then {{{...{{{ }}}...}}} with n+1 curly brackets ∈ Z₀
>
and
>
The set of FISONs failing to have
the union ℕ defied by induction:
|ℕ \ {1}| = ℵo, and
if |ℕ \ {1, 2, 3, ..., n}| = ℵo
then |ℕ \ {1, 2, 3, ..., n+1}| = ℵo.

 For the second,
I have elsewhere provided you with
the description of a FISON

Where?

For the first,
you aren't using
any definition which fills
a role comparable to "FISON'.

Wrong. {{ }} = {1}, {{{ }}} = {1, 2}, {{{{ }}}} = {1, 2, 3}.

I can see that you aren't because
you think you have defined 'finite' there,

All FISONs are finite.

somehow (by a darkᵂᴹ definition?),
and because
you have said explicitly that you don't need
a definition elsewhere.

Before you recognized that you have run out of counterarguments you never doubted that definition.

 You (WM) think you don't need to say
what natural number is,
even where you clearly have taken the term
and used it in your own, private way.

I use definable natumbers as everybody knows how to use them.
Regards, WM