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Topic: Matheology § 253
Replies: 30   Last Post: Apr 22, 2013 2:44 PM

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Posts: 18,076
Registered: 1/29/05
Re: Matheology § 253
Posted: Apr 21, 2013 10:13 AM
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On 19 Apr., 22:50, Virgil <> wrote:

> > There exist m, n, a, b in |N,
> > such that m is in FISON(a) and not in FISON(b) and n is in FISON(b)
> > and not in FISON(a).

> For each natural n in |N, FISON(n) is defined by WM to be the set of all
> naturals less than or equal to the natural number n.
> Thus for natural numbers m ands n,
> n is in FISON(m)  if and only if  n <= m, and
> similarly n is NOT in FISON(m)  if and only if  m < n.
> Thus if m is in FISON(a) and not in FISON(b), then b < m <= a
> and if n is in FISON(b) and not in FISON(a), then a < n <= b
> Thus in WM's world one must have b < a and a < b simultaneously.

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. 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"


Regards, WM

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