Re: The set of necessary FISONs

On 10.03.2025 18:47, Jim Burns wrote:

On 3/10/2025 1:20 PM, WM wrote:

On 10.03.2025 17:31, Jim Burns wrote:

On 3/10/2025 4:42 AM, WM wrote:

 

For example, here:
⎛ A  FISON is linearly ordered,
⎜ begins at 0, ends at a FISON.end,

>
That is sufficient.

 The real interval [0,x] is linearly ordered,
begins at 0, and,
if [0,x] is a FISON, ends at a FISON.end.

Why can't you stay with the topic?! Do you suffer from attention deficit disorder?

 A real interval isn't what you mean by 'FISON'
is it?

Stop with that waffle!

Peano and Zermelo and Cantor and I
describe infinitely.many.

>
Yes, without end.

 The descriptions end.

The sets don't.

 What is described is without end.
 Not.first.false claims are true
about what does not end
because _the descriptions_ end (are finite).
 Because _the claims_ are finitely.many,
if there is a false claim,
then there is a first.false claim.

Z₀ is defined by induction: { } ∈ Z₀, and if {{{...{{{ }}}...}}} with n curly brackets ∈ Z₀ then {{{...{{{ }}}...}}} with n+1 curly brackets ∈ Z₀.
Likewise the removable UF is defined by induction.
ℕ \ F(1), and if ℕ \ F(1) \ F(2) \ F(3) \ ... \ F(n) = ℵo
then ℕ \ F(1) \ F(2) \ F(3) \ ... \ F(n+1) = ℵo.
What is the difference in your opinion?
Regards, WM