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:

set operations

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.

Section 5.1.2, "A formal definition of relations," pages 251-253
Chapter 6, "Functions and cardinality," Section 1, "Functions," pages 319-325

[external website]

Author: Keith Schwarz

-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