Definition:Ordered Pair

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.

It is written $$\left({a, b}\right)$$ and it means "first $$a$$, then $$b$$".

It can be formalised by the definition:

$$\left({a, b}\right) = \left\{{\left\{{a}\right\}, \left\{{a, b}\right\}}\right\}$$