In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> 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.
In every ennumeration it will be the 99th set, but in different ennumerations it will be usually a different one of the original set. > > Every definable set of natural numbers has a first element.
Only if their overall ordering is required to be a well ordering.
But if one bijects the naturals with the members of an open interval of rationals and imposes the ordering of those rationals back onto the naturals, for the resulting ordered set of naturals it is no longer true.
> And there > can be no question that
Whenever there is a formidableborder like that between Wolkenmuekenheim and the world, there will be considerable questions about everything until it has been made clear from which side of that border one is looking.
WM can control only what he allows himself to see from his side, but has no control over what anyone on the other side can see. --