Course MA2C03, Michaelmas Term 2014 Section 1: Sets and Functions

1 Sets and Functions 1 1.1 Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Unions, Intersections and Complements of Sets . . . . . . . . . 1 1.3 Subsets and Power Sets . . . . . . . . . . . . . . . . . . . . . . 3 1.4 The Specification of Sets . . . . . . . . . . . . . . . . . . . . . 5 1.5 Binary Relations . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.6 Congruences . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.7 Partitions and Equivalence Relations . . . . . . . . . . . . . . 9 1.8 Partial Orders and Lattices . . . . . . . . . . . . . . . . . . . 10 1.9 Cartesian Products of Sets . . . . . . . . . . . . . . . . . . . . 11 1.10 Functions between Sets . . . . . . . . . . . . . . . . . . . . . . 13 1.11 Compositions of Functions . . . . . . . . . . . . . . . . . . . . 14 1.12 The Graph of a Function . . . . . . . . . . . . . . . . . . . . . 14 1.13 The Inverse of a Function . . . . . . . . . . . . . . . . . . . . 15 1.14 Injective, Surjective and Bijective Functions . . . . . . . . . . 16 1.15 Functions defined on Finite Sets . . . . . . . . . . . . . . . . . 19