An ordered pair is a 2-tuple formed by taking two elements (generally numbers but can be alphabets, characters, words, or symbols).

The general form of representation is (a, b) where a and b represent two distinct objects.

The important thing with ordered pairs is that the ordering of the participating elements is important i.e. (a, b) is different from (b, a) unless a=b

(a,b) ≠ (b,a) unless a=b

Examples of Ordered pairs :

(1,2)
(a,b)
(-172,45.98)
(x,3)

Remember ☞

• (a, b) ≠ (b, a), unless a = b. 

• If (a1, b2) = (a2, b2) ⇒ a1=a2 & b1=b2

Ordered pairs are widely used in set theory, calculus, relations, and function theories and in the representation of intervals for functions on numbers lines, and axis, for laws and theories in mathematics, physics, chemistry, biology, statistics, etc.