```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 everystudent 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 givensets that, when removed, changesthe union.Examples involving crayon marksshall be left to others.
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