Course 2BA1: Michaelmas Term 2006 Section 5: Sets and Functions

5 Sets and Functions 1 5.1 Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 5.2 Unions, Intersections and Complements of Sets . . . . . . . . . 2 5.3 Subsets and Power Sets . . . . . . . . . . . . . . . . . . . . . . 4 5.4 The Specification of Sets . . . . . . . . . . . . . . . . . . . . . 6 5.5 Binary Relations . . . . . . . . . . . . . . . . . . . . . . . . . 7 5.6 Congruences . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 5.7 Partitions and Equivalence Relations . . . . . . . . . . . . . . 9 5.8 Partial Orders and Lattices . . . . . . . . . . . . . . . . . . . 11 5.9 Cartesian Products of Sets . . . . . . . . . . . . . . . . . . . . 13 5.10 Functions between Sets . . . . . . . . . . . . . . . . . . . . . . 15 5.11 Compositions of Functions . . . . . . . . . . . . . . . . . . . . 16 5.12 The Graph of a Function . . . . . . . . . . . . . . . . . . . . . 16 5.13 The Inverse of a Function . . . . . . . . . . . . . . . . . . . . 17 5.14 Injective, Surjective and Bijective Functions . . . . . . . . . . 18 5.15 Partial Mappings . . . . . . . . . . . . . . . . . . . . . . . . . 21