Set Theory. Relations, Functions, and Countability. Relations. Let B ( n ) denote the number of equivalence relations on n elements. Show that B(n) ≤ . Show that B(n) ≤ n!. Show that B(n) ≥ 2 n−1 . . Bell numbers. Functions and Equivalence Relations. Remark
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Relations, Functions, and Countability
Equivalence relation is a relation that is reflexive, symmetric, and transitive
where Δ(x, y) denotes the Hamming distance of x and y,