Lecture 5
Composition of maps, an associative law for composition. Further properties relating to composition of one-to-one, onto and bijective maps. Definition of the set of all one-to-one mappings.
Lecture 6
Maps and functions. Examples. Introduction to the set of integers. Associativity, commutativity, existence of an identity and inverse under addition. Associativity, commutativity, existence of an identity under multiplication. Least integer principle.
Lecture 7
Uniqueness of least integer. The principle of induction. The Euclidean Algorithm. The greatest common divisor: definition, uniqueness and existence.
Lecture 8