Introduction to sets

Membership relation

Axiom of extensionality

Equivalence classes

Defining sets

Axiom schema of specification

Implications of axiom schema of specification

Set-builder notation

Empty set

Defining sets by enumeration

Finite and infinite sets

Cardinality

Ordering

Inequalities

Ordered sets

Intervals

Infinitum, supremum, minimum and maximum

Set algebra

Set union and intersection

Complement and disjoint sets

Axiom of union

Boolean algebra

Algebra on a set

Natural numbers

Axiom of infinity

Cardinality of the natural numbers

Ordering of the natural numbers

Subsets and powersets

Subset relation

Powerset

Cantor's theorem

Tuples

Tuples

Axiom of pairing

Cartesian product

Direct sums

Functions

Constructing functions

Domains and ranges

Axiom of regularity