Ordered pair

An ordered pair $(a,b)$ is an object determined by two entries $a$ and $b$ such that

Ordered pairs are the building blocks of Cartesian products, graphs of functions, and relations. The defining property above is what distinguishes an ordered pair from a 2-element set, where order is irrelevant.

Examples:

• $(1,2)\neq(2,1)$.
• In $\mathbb{R}^2$, a point is an ordered pair $(x,y)$ with $x,y\in\mathbb{R}$.
• The graph of $f(x)=x^2$ is $\{(x,x^2):x\in\mathbb{R}\}\subseteq\mathbb{R}\times\mathbb{R}$.