---
tag: 0JQWWFCS9R
kind: definition
name: Ordered pair
msc: ["03E20"]
defines: 0WFCNG0MZC
uses: [0SJ3RX9TXA]
sources:
  - url: https://en.wikipedia.org/wiki/Ordered_pair
    locator: lead section
---

## Definition

An ordered pair $(a, b)$ has a first entry $a$ and a second entry $b$, with this property:
$$(a, b) = (c, d) \iff a = c \text{ and } b = d.$$
In set theory, the Kuratowski definition is $(a, b) = \{\{a\}, \{a, b\}\}$. It has the property above.

## Remarks

In general $(a, b) \neq (b, a)$, but the sets $\{a, b\}$ and $\{b, a\}$ are equal.
Ordered pairs are the elements of a [[Cartesian product|0C81YBVTWH]].
An ordered triple can be defined as $(a, b, c) = ((a, b), c)$.

## Explanations

### L1 human

A point in the plane is an ordered pair of coordinates.
The points $(1, 2)$ and $(2, 1)$ are different, so the order matters.
The Kuratowski definition only shows that sets can model pairs.