Re: The set of necessary FISONs

On 02.02.2025 18:41, joes wrote:

Am Sun, 02 Feb 2025 12:06:26 +0100 schrieb WM:

On 01.02.2025 19:42, joes wrote:

Am Sat, 01 Feb 2025 14:40:12 +0100 schrieb WM:

Mathematical induction is a method for proving that a statement P(n) is
true for every natural number n that is, that the infinitely many cases
P(0),P(1),P(2),P(3),... all hold. [Wikipedia]

And you want the wrong P(ω) to hold, but you cannot remove infinitely
many segments.

What does Peano create by n => n+1? Is it all natural numbers?
Why does induction n => n+1 not cover all FISONs.

This is different from all P(n) which together say
you can remove any finite *number of* segments (not the segments
themselves).

What is the difference to Peano?

Do you get that?

Not yet. I cannot see a difference between Peano's application of n => n+1 and my application of n => n+1.

There is no infinite segment, but
there *are* infinitely many.

Like the natural numbers created by Peano? Does he create the set ℕ? Does Zermelo by the same technique create the set ℕ?
Regards, WM