Subsets of Set of Real Numbers

Subsets of Set of Real Numbers

Real numbers are defined as the collection of all rational numbers and irrational numbers, denoted by R. Therefore, a real number is either rational or irrational.

The set of real numbers is: R = {…-3, -√2, - $\frac{1}{2}$12  , 0, 1,  $\frac{4}{5}$45  , 16,….}

Some of the apparent relations among these subsets are:

N ⊂ W ⊂ Z ⊂  Q ⊂ R,     T ⊂ R,      N ⊄ T.

As real numbers consist of rational numbers and irrational numbers, we can say that integers, whole numbers and natural numbers are also the subsets of real numbers. This relation can also be understood from the below figure.