Date: Mar 24, 2013 4:50 AM
Subject: Re: Matheology § 224

On 24 Mrz., 02:30, Virgil <> 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

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.

Regards, WM