Ordered Pairs and Equality of an Ordered Pairs

ByGet Way Learning

Ordered pairs

               An ordered pairs consists of two objects or elements in a given fixed order. 

For example, if A and B are any two sets, then by an ordered pair of elements we mean a pair (a, b) in that order, where a ∈ A, b ∈ B.
NOTE  
An ordered pair is not a set consisting of two elements. The ordering of the two elements in an ordered pair is important and the two elements need not be distinct.
Example
The position of a point in a two dimension plane in cartesian coordinate is represented by an ordered pair. Accordingly, the ordered pairs (1, 3),(2, 4),(2, 3) and (3, 2) represents different points in a plane.

Equality of an ordered pairs

Two ordered pairs (a1, b1) and (a2, b2) are equal iff (if and only if) a1=a2 and b1=b2.
i.e.          (a1,   b1) = (a2, b2) ⇔a1 = a2 and b1 = b2
It is evident from this definition that (1, 2) ≠ (2, 1) and (1, 1) ≠ (2, 2).


Similar Posts

Introduction about Thermodynamics and Application of Thermodynamics

ByGet Way Learning

Introduction about thermodynamics Energy is the capacity to do work energy cannot be created or destroyed but only can be changed into other forms (principle of conservation of energy). Thermodynamics mainly deals with interaction between heat and work (mechanical energy) and change in the property is associated with these interactions. The interaction between heat and…

Properties of Ideal gases ∣ Charactaristic of gas equation ∣ Specific Heat

ByGet Way Learning

Ideal gases       The term gas is applied to a particular phase of a pure substance which will fills the system boundary, and no change of phase takes place or is contemplated. They always exist in gaseous form. For this reason, they have been called permanent gases.           Perfect…

Leave a Reply

Your email address will not be published. Required fields are marked *