A Theory of Partitions . Part I Shunichi
نویسندگان
چکیده
Let us consider S1, S2. We introduce S1 b S2 and S2 c S1 as synonyms of S1 is finer than S2. The following four propositions are true: (3)1 ⋃ (S1 \{ / 0}) = ⋃ S1. (4) For all partitions P1, P2 of Y such that P1 c P2 and P2 c P1 holds P2 ⊆ P1. (5) For all partitions P1, P2 of Y such that P1 c P2 and P2 c P1 holds P1 = P2. (7)2 For all partitions P1, P2 of Y such that P1 c P2 holds P1 is coarser than P2.
منابع مشابه
A Theory of Partitions . Part I
For simplicity, we use the following convention: Y is a non empty set, P1, P2 are partitions of Y , A, B are subsets of Y , i is a natural number, x, y, x1, x2, z0 are sets, and X, V , d, t, S1, S2 are sets. The following proposition is true (1) If X ∈ P1 and V ∈ P1 and X ⊆ V, then X = V. Let us consider S1, S2. We introduce S1 ⋐ S2 and S2 ⋑ S1 as synonyms of S1 is finer than S2. We now state s...
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