Equivalence Relations

Definition

Examples

Modular Arithmetic

Modular Arithmetic

Equivalence Classes

Equivalence Classes

Properties of Equivalence Classes

An Important Equivalence Relation

An Important Equivalence Relation

Partitions

Partitions

Theorem 3.6

Theorem 3.6

Order Relations

Partial Orders

Predecessors

Hasse Diagrams

Hasse Diagrams

Supremum

Infimum

Example

Theorem 3.8

Largest and Smallest Elements

Largest and Smallest Elements

Total Orders

Total Orders

Well Ordering

Well Ordering