\begin{definition}[Definition:Ordered Pair/Informal Definition]
The definition of a set does not take any account of the order in which the elements are listed.
That is, $\set {a, b} = \set {b, a}$, and the elements $a$ and $b$ have the same status -- neither is distinguished above the other as being more "important".
An '''ordered pair''' is a two-element set together with an ordering.
In other words, one of the elements ''is'' distinguished above the other - it comes first.
Such a structure is written:
:$\tuple {a, b}$
and it means:
: '''first $a$, then $b$'''.
\end{definition}