Ordered Pair

A pair $(a,b)$ of numbers, where the ORDER in which the numbers appear matters, is called an ORDERED PAIR. The ordered pairs $(a,b)$ and $(b,a)$ are generally different (unless $a=b$). In the ordered pair $(a,b)$, 'a' is called the FIRST COMPONENT and 'b' is called the SECOND COMPONENT.

Two key facts about equality of ordered pairs: (i) $(a,b)=(c,d)$ if and only if $a=c$ AND $b=d$ — both components must match individually; (ii) $(a,b)=(b,a)$ if and only if $a=b$ — the pair only 'looks the same reversed' when both components are actually equal. …