# equivalence relations

## Summary

A relation is an equivalence relation if it is reflexive, symmetric, and transitive. Equivalence relations can be used to partition a set into equivalence classes. Examples include equality, isomorphism, and graph connectivity.

## Context

-this concept has no prerequisites-

## Goals

- Define an equivalence relation

- Be able to show that something is an equivalence relation

- Understand how equivalence relations partition a set into equivalence classes

## Core resources (read/watch one of the following)

## -Free-

→ Stanford CS103: Mathematical Foundations of Computing (2013)

Lecture notes for Stanford's introductory computer science theory course.

## -Paid-

→ Elements of Set Theory

An introductory textbook on axiomatic set theory.

Location:
Chapter 3, "Relations and functions," subsection "Equivalence relations," pages 55-62

## See also

-No Additional Notes-