Re: The set of necessary FISONs

Am Mon, 10 Mar 2025 09:42:05 +0100 schrieb WM:

On 10.03.2025 00:11, Jim Burns wrote:

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

 

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}.

This is wrong as written. Perhaps you mean equivalences, but they are
certainly not equal.

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.

Not an argument. What's the 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.

You can't hide your personal usage behind "everybody knows". If every-
body knows, show it.

--
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.