Examples The of { x, y, z } by , has the Hasse diagram: The A = { 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 } of all divisors of 60, partially ordered by , has the diagram: The set of all 15 of the set { 1, 2, 3, 4 }, partially ordered by refinement (i.e. a finer partition is "less than" a coarser partition), has the Hasse diagram: Functions Definitions on Functions: A function, denote it by from a set to a set is a relation from to that satisfies f, A B A B for each element in there is an element in such that <a, is in the relation, and a A, b B b> if <a, and <a, are in the relation, then . b> c> b = c
Examples The of { x, y, z } by , has the Hasse diagram: The A = { 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 } of all divisors of 60, partially ordered by , has the diagram: The set of all 15 of the set { 1, 2, 3, 4 }, partially ordered by refinement (i.e. a finer partition is "less than" a coarser partition), has the Hasse diagram: Functions Definitions on Functions: A function, denote it by f, from a set A to a set B is a relation from A to B that satisfies for each element a in A, there is an element b in B such that <a, b> is in the relation, and if <a, b> and <a, c> are in the relation, then b = c .
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