Re: The set of necessary FISONs

On 16.02.2025 12:59, joes wrote:

Am Sun, 16 Feb 2025 12:18:28 +0100 schrieb WM:

If all FISONs are omissible by induction, then the
set of all FISONs is omissible.

That is simply false.

Show what should remain.

And why? Note that you must define a first element.

Indeed, why should something remain if you remove everything?

Everything is removed that can be removed without changing the result.

There is no doubt that this proves the whole set Z without assuming a
last element.

WDYM „prove a set”?

"In order to secure the existence of infinite sets, we need the following axiom." [Zermelo] This is the axiom of infinity or induction: { } and if a then {a}.
Regards, WM
  For every *element* you can prove the statement

„This, and only this segment can be omitted.” Unfortunately there
is no element that encompasses all numbers.