# functions and relations as sets

## Summary

Ordered pairs, relations, and functions can all be defined in terms of sets. This is part of why set theory is such a powerful framework in the foundations of mathematics.

## Context

This concept has the prerequisites:

## Goals

- Define ordered pairs, functions, and relations in terms of sets

- Show that the definitions correspond with our intuitions for how these objects should behave

## 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," up through subsection "Functions," pages 35-54

## See also

-No Additional Notes-