# order relations

## Summary

A relation is an order relation if it is irreflexive, asymmetric, and transitive. An order relation < is a total order if for any A and B, either A < B, B < A, or A = B; otherwise it is a partial order.

## Context

This concept has the prerequisites:

- equivalence relations (The definition of order relations parallels that of equivalence relations.)

## Goals

- Define order relation

- Know the distinction between total orders and partial orders

- Be able to show that something is total or partial order

- Know the distinction between maximal element and largest element

## 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.

Location:
Section 5.3, "Order relations," up through 5.3.3, "Hasse diagrams," pages 271-286

## -Paid-

→ Elements of Set Theory

An introductory textbook on axiomatic set theory.

- Chapter 3, "Relations and functions," subsection "Ordering relations," pages 62-64
- Chapter 7, "Orderings and ordinals," subsection "Partial orderings," pages 167-172

## See also

-No Additional Notes-