Date: Mar 24, 2013 9:42 AM
Author: fom
Subject: Re: Matheology § 224
On 3/24/2013 3:50 AM, WM 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.

>

He is talking about the kind of "set" that every

student in mathematics (except, perhaps, yours)

learns about.

He is not talking about the theory of

"monotonic-inclusive crayon marks".

10 sets:

{1,2,3,4,5,6,7,8,9}

{0,2,3,4,5,6,7,8,9}

{0,1,3,4,5,6,7,8,9}

{0,1,2,4,5,6,7,8,9}

{0,1,2,3,5,6,7,8,9}

{0,1,2,3,4,6,7,8,9}

{0,1,2,3,4,5,7,8,9}

{0,1,2,3,4,5,6,8,9}

{0,1,2,3,4,5,6,7,9}

{0,1,2,3,4,5,6,7,8}

union of 10 sets:

{0,1,2,3,4,5,6,7,8,9}

Pick a set from the 10 given

sets that, when removed, changes

the union.

Examples involving crayon marks

shall be left to others.