Concept:

A branch of mathematics which deals with symbols and the rules for manipulating those symbols is called algebra. Those symbols which represent quantities without fixed values known as variables.

Given:

The objective is to give an explanation to the set of counting , whole, integer, rational, irrational, real numbers and the related to each other

Thus all the counting numbers are whole numbers

where,

W=0,1,2,3,..

the counting numbers are 1,2,3,...

The integers are whole numbers

...-3,-2,-1,0,1,2,3,....

The rational numbers are quotients of the integer

\(1/2,6,6/7,....\)

Irrational number are that where the it is not possible to right the quotients of the integer

\(\pi=\sqrt2\)

It known that the real numbers are either rational or irrational numbers and the real numbers are the larger set of rational or irrational numbers where rational and the irrational numbers are subsets.

A subset of rational numbers are subsets whereas for integer it is whole number and the subset for whole number is counting numbers.