Re: The set of necessary FISONs

On 2/18/25 10:22 AM, WM wrote:

On 18.02.2025 13:25, Richard Damon wrote:

On 2/18/25 4:53 AM, WM wrote:

On 18.02.2025 04:02, Richard Damon wrote:

On 2/17/25 2:25 PM, WM wrote:

>

A set without elements is an empty set and not capable of producing ℕ.

>

But an empty set of REQUIRED elements doesn't mean we can't have a set of sufficient elements.

>
There is no element that could be a meaningful member of any sufficient set. Therefore there is no sufficient set.

 

Of course there are, its just they are not individually needed, but are collectively sufficient.

 For every FISON there is the question: Can it belong to a collectively sufficient set. For every FISON the answer is no.
 Regards, WM
 

No, for sufficiency, the answer is YES. For instance the set of all FISONs ending in a even number, or all FISONs ending in an odd number are each sufficient sets, and every FISON will belong to one of them.
Does it belong to a NECESSARY set has the answer no, but then there doesn't need to be one.
You are just confused.