Re: The set of necessary FISONs

On 16.02.2025 23:43, Jim Burns wrote:

On 2/15/2025 9:51 AM, WM wrote:

On 14.02.2025 19:06, Jim Burns wrote:

 

The set of all natural numbers is not.in
the only inductive subset of the set of
all natural numbers.

>
The set of all natural numbers is constructed
by induction.

 By axiom "infinity",
an inductive set exists.

The axiom applies induction.

If the set with an only.inductive.subset
was an element, we'd prove the set has P.
But the set isn't an element.
We don't prove the set has P.

Sometimes this is right, sometimes it is wrong.
When all elements of a set are subject to induction then the set is an inductive set.
When all elements of a set are removed, then the set is removed.
Example:
If every human has an end, then the human race need not have an end.
If every human has ended, then the human race has ended.
Regards, WM