Cartesian products and Relations (domain, range, inverse, composition), Equivalence relations and Partitions, Ordering Relations (POSETS and Totally Ordered Sets). Functions (domain, codomain, range equality of functions, many examples), Injective, surjective, and bijective functions, Inverses and inverse functions, Images and inverse images of sets in a function, functions and inverses on unions and intersections and complements, Restriction functions on a subset (and restricting the codomain to the range), Composition of functions (composing a function with its inverse), Equipotent sets, Finite and infinite sets, Countable and Denumerable Sets, Proof of countability of Q, Examples and properties of denumerable sets, Nondenumerable sets and properties, Proof of uncountability of R, The concept of cardinal numbers, Cardinal number of a power set, Cantor's theorem, addition and multiplication of cardinal numbers.