Re: The set of necessary FISONs

On 15.02.2025 14:47, Richard Damon wrote:

On 2/15/25 6:50 AM, WM wrote:

On 14.02.2025 19:02, Richard Damon wrote:

On 2/14/25 11:28 AM, WM wrote:

>

The definition is that it is a set of FISONs which has a smallest element that is not as useless as a cup of coffee.

>

Which, as I said, is a definition in Naive Set theory,

>
Obviously you have no clue of set theory, be it naive or advanced.
Every set of ordinals has a smallest element. Look up the notion of well-order.

Every NON-EMPTY set of Ordinals has a smallest element.

So it is.

 The problem is your "claimed set" can't actually defined in anything but Naive set theory,

It is defined in modern set theory.

and the fact that you admit that it might be needed shows you have an understanding of the problem.

Of course, better than you.

 The set you can actually define, is the set of FISONs that are individually required to build up a set that can union to the Natural Numbers, but that CAN be empty, and we can still make a set that reaches there.

No, that would imply that it is meaningful to replace a removed FISON by smaller FISONs.
Regards, WM