Re: The set of necessary FISONs

On 3/1/25 1:09 PM, WM wrote:

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

And what SET did that build? P was a statement about a relaitonship.
Your source doesn't prove what you claim.

>
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.

No, you are in error. You can try to claim that the system it creates is inconsistent, but to do so you need to show the error using the system as defined. Since you can't do that, as your mind can't handle the logic, you are stuck having to admit that you just can't work in that system. Since your "logic" is Naive, and not actually based on the formal rules you try to disparage as "Mathologies", you have stripped yourself of the ability to show what you claim, and just prove that your Naive Logic is itself inconsistant when you try to use it on infinite sets like the Natural Numbers.
That doesn't show that the axiom of infinity is in error, it shows that your own logic is in error when streached to look at infinite sets, which it can not handle.

 

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.

Yes it is. Of course if you deny that infinity exists, then everything that is actually infinite won't seem right to you, but the problem is yours.
All you have done is shown that you don't believe in the existance of the Natural Numbers as defined, and thus anything you have done base on a claim with the natural numbrs (like your FISONs) you have just admitted is based on lies.

 Regards, WM