```Date: Apr 22, 2013 3:00 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 253

On 21 Apr., 22:25, Virgil <vir...@ligriv.com> wrote:> > Explain how N elements (n) can be distributed, with repetition, among> > M sets (s_k) such that there are all elements n represented at least> > once, all s_k are used too, but not all elements n are in in one set> > s_k.>> WM himself has shown us how to do it:>> FISON_1 = s_1 = { 1 }> FISON_2 = s_2 _ { 1 2 } = { 2 1 }> FISON_3 = s_3 = { 1 2 3 } = { 3 2 1 }> ...>> So FISONs do it very neatly!No, you have not shown the other condition, namely that all naturalsare in those FISONs.>> > Is it possible to avoid the condition:> > exist  j, k, m, n : m e s_j & ~(m e s_k) & ~(n e s_j) & n e s_k"?>> Yes! Trivially! it is, in fact, impossible for any 4 naturals> j, k, m, n not to avoid it.That is correct.>>>> > How?>> How not?>> See above.You have not shown the other condition, namely that all natural are inthe FISONs.>> Also. from a previous post:>> WM's claim:>> > If *not* all naturals in one s, then> > exist j, k, m, n : m e s_j & ~(m e s_k) & ~(n e s_j) & n e s_k.that is obvious in mathematics if two conditions have to hold:1) All naturals in FISONs.2) Not all naturals in one and the same FISONs.Regards, WM
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