Re: The set of necessary FISONs

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?

 

The process cannot be completed with FISONs. Each one is finite, and so is their potentially infinite number. That does never change.
>

It can not be completed with a finite number of them. It can be completed with the complete set of them.

 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}
...
 Regards, WM
  

Nope, the axion of Induction (which needs the axiom of infinity) says that the process DOES complete.
You are just showing you don't know what the terms mean.
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,
I guess you are just showing that you have defined yourself into a hole that just shows you aren't taking about what you are trying to talk about because you are just mis-using terminology.