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 naturals

are 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 in

the 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