Re: The set of necessary FISONs

On 2/11/25 5:05 AM, WM wrote:

On 11.02.2025 01:03, Richard Damon wrote:

On 2/10/25 10:00 AM, WM wrote:

 

Does Zermelo define a set by induction or only its elements?
>

Zermelo BUILDS a set by creating its members.

 So do I.

But it isn't the set you need. You build up the set of FISONs that are not individually needed, then somehow magically create with that a set of FISONs you can use to do the task.
Sorry, that logic says that you can't factor 36.

 

Note, you keep on confusing a property of the members for a property of the set.

 There is a set {1} smaller than ℕ.
If the set {1, 2, 3, ..., n} including its predecessors is smaller than ℕ, then the set {1, 2, 3, ..., n+1} including its predecessors is smaller than ℕ.

So, none of that does anything about the set of FISONs available to build up the set N.

No individual FISON is required to build a set of FISONs whose union is the set of Natural Numbers,

 No FISON is available. All FISONs belong to the inductive set F of insufficient FISONs. There is no FISON remaining.

And thus you can't factor 36, as none of factors of 36 are required either.
Again, you created out of thin air this set of "available" FISONs.
You built that by SUBTRACTION, which isn't what you said, showing you are so stupid you just naturally lie about thingsl
Your building process wasn't based on what can be available, just which individuals aren't individually needed.

 

but that doesn't mean the set of FISONs you CAN use is empty.

 No, but it means: IF U(F) = ℕ, THEN { } = ℕ,

Nope, just that you are too stupid to know the difference between Necessary and Sufficent, and too stupid to see that stupidity.

 Regards, WM