On 24 Mrz., 02:30, Virgil <vir...@ligriv.com> wrote:
> Given: that deleting anyone set from a union of sets does not decrease > the union the set of remaining sets, > > THEN: Decreasing that union will require, if possible at all, deleting > more than one member set, but deleting more than one member set still > may not alsays decrease the union. > > Example: 100 different subsets each of 99 elements out of their union of > 100 elements. Then the union of the set of any two or more of them > equals the union of the set of all 100 of them.
Enumerate the sets. Then there will be a first set that, when subtracted from the union, will change the union of the remaining sets.
Every definable set of natural numbers has a first element. And there can be no question that FISONs that do not change the union of all FISONs are well defined.