ordered pair of real numbers

Ordered pair of real number

Ordered pair of real numbers: An ordered pair of real numbers x and y in which element are written in specific order.

(i) (x, y) an ordered pair in which the first element is x and the second is y. such that (x, y) ≠ (y, x) where x ≠ y.

Ordered pair of real number

(ii) (2, 3) and (3, 2) are two different ordered pairs.

(iii) (x, y) = (m, n) only if x = m and y = n

Recognizing an ordered pair:

In the Examination room, the chair of a student is the example of ordered pair. For example, the chair of the student A is 5th place in the third row. It makes the ordered pair (3, 5). Here 3 show the number of the row and 5th show the chair number.

Numeric Example;

An ordered pair (6, 7) represent x value is equal to 6 in row or x = 6 and y value equal to 7 or y = 7 in column.

By definition of ordered pair  (6,7) ≠ (7, 6) 

Ordered pair in Cartesian plane :

A Cartesian plane shows one to one correspondence between the set of ordered pair R × R = {(x, y) ∈ R}