Definition:Ordered Pair/Informal Definition

Definition
The definition of a set does not take any account of the order in which the elements are listed.

That is, $\left\{{a, b}\right\} = \left\{{b, a}\right\}$, 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:
 * $\left({a, b}\right)$

and it means:
 * first $a$, then $b$.

Also see

 * Equivalence of Definitions of Ordered Pair