Re: The set of necessary FISONs

On 01.03.2025 17:25, Richard Damon wrote:

On 3/1/25 9:31 AM, WM wrote:

On 28.02.2025 20:45, Richard Damon wrote:

On 2/28/25 11:44 AM, WM wrote:

>

No, Zermelo uses induction. I did not say that he uses the term induction.

>
No, what you describe is NOT "induction".

>
Correct your qualifiers. Or look it up.
F(1) ∈ F and F(n) ∈ F ==> F(n+1) ∈ F describes the infinite inductive set F of FISONs.

 You have a source that uses the term "Induction" for the recursive iteration that builds the set?

∀P(P(0) /\ ∀k(P(k) ==> P(k+1)) ==> ∀n (P(n)))
Wikipedia

>
Processes using defined individuals like FISONs cannot surpass a finite set. FISONs are finite. Their number will never be greater than finite.
{1}
{2, 1}
{3, 2, 1}
...

 > Nope, the axion of Induction (which needs the axiom of infinity) says
 > that the process DOES complete.
It is in error.

Since F(0) exists, and the existance of F(n) says that F(n+1) exist, the axion of induction says that F(m) exist for ALL m a member of the Natural Numbers, and thus the set of FISION is infinite,

Not actually infinite.
Regards, WM