On 19 Apr., 22:50, Virgil <vir...@ligriv.com> 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" ?