This section contains foundational definitions from set theory and mathematical logic used throughout analysis and algebra.
Sets and Set Operations
- Set
- Empty set
- Subset
- Proper subset
- Union
- Intersection
- Set difference
- Complement
- Symmetric difference
- Power set
- Cartesian product
- Ordered pair
- Indexed family of sets
- Partition
Functions
- Function (map)
- Domain
- Codomain
- Image
- Preimage
- Graph of a function
- Restriction
- Composition
- Identity function
- Inverse function
- Injective function
- Surjective function
- Bijective function
- Sequence
Relations
Order
Number Systems
Cardinality
Operations
Axioms and Principles
- ZFC axioms
- Axiom of Choice
- Mathematical induction
- Well-ordering principle
- Well-ordering theorem
- Zorn's lemma