Date: Mar 24, 2013 4:50 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 224
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.

Regards, WM