Re: The set of necessary FISONs

WM expressed precisely :

On 28.01.2025 10:29, FromTheRafters wrote:

WM wrote on 1/28/2025 :

On 27.01.2025 16:23, FromTheRafters wrote:

WM wrote :

On 27.01.2025 15:14, joes wrote:

Am Mon, 27 Jan 2025 12:35:56 +0100 schrieb WM:

On 26.01.2025 23:31, Richard Damon wrote:

>

you can't show that the first FISON isn't a member of the set of
necessary FISONs without assuming the set of necessary FISONs exists.

>
Logic? The set ℕ exists. And I can show that every FISON is neither
necessary nor sufficient to accomplish that aim.

Obviously, but not for infinite sets of FISONs.

>
Also an infinite set needs a first element.

>
The real numbers are an infinite set, which one is first?

>
Here we talk about FISONs.

 You said 'an infinite set needs a first element' and FISONs are not infinite sets.

>
An infinite set of FISONs that has the union ℕ needs a first element.

It has one defined already, the initial element. That is, if you mean 'An infinite *ordered* set of FISONs' the empty set is the first FISON in the natural order of natural numbers.