Subsets of Real Numbers

Following are the subsets of real numbers

Natural Numbers

It is the set of numbers used for counting fall under natural numbers .It is represented by N

N= { 1, 2, 3 , 4 … }

Whole Numbers

It is the set of numbers that include zero and set of natural numbers is set of whole numbers. It is represented by W.

W= { 0 , 1 , 2 , 3 , 4… }


It is the set of numbers that include zero , set of natural numbers (positive integers) and set having opposite natural numbers ( negative integers).

Z= { … ,-3 , -2 , -1 , 0 , 1,2 , 3, … }

Rational Numbers

It is the set of numbers which include integers that can be written in fraction form a / b where b is non-zero integer .The decimal expansions of rational numbers include recurring , terminating or both features. It represented by Q .

Irrational Numbers

It is the set of numbers which can’t be written in fraction form and include non-terminating and non-recurring decimals. It is represented by Q. This subset of real numbers is greater in infinity than rational numbers


Generally , the set of real numbers is shown as
subsets of real numbers formula

Where ℝ is used to represent all real numbers and the symbol ‘ ∪ ‘ is used to represent the union of two sets.

Now let’s learn is pi a real number and is 0 a real number.

Let's find out is Pi a Real Number ?

Yes , pi is a real number as

pi= 3.14159256 …. having non-recurring and non-terminating decimal is an irrational number.

Also, let's check is 0 a Real Number ?

Yes , 0 is a real number as it’s a rational number

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