Number System

Natural Numbers (N):

                The numbers starts from 1, 2, 3 ... etc; are called Natural numbers. Natural numbers are denoted by ‘N’.

N= {1, 2, 3 …}

Whole Numbers (W):

The numbers starts from 0, 1, 2, 3 ... etc; are called Whole numbers. Whole numbers are denoted by ‘W’.

W= {0, 1, 2, 3 …}

Integers (I or Z):

The numbers etc…, -3,-2,-1, 0, 1, 2, 3 … etc; are called Integers. Integers are denoted by I or Z.

Z= {…, -3,-2,-1, 0, 1, 2, 3 …}

Rational Numbers (Q):

The numbers which can be written in the form of p/q, q≠0, where p and q are integers are called Rational numbers. Rational numbers are denoted by ‘Q’.

Examples: ⅓, ⅔,-⅕, ⅖,-⅘, ⅜,-⅞, 0,-1,-2,-3,-4, 1, 2, 3, 4 … etc

Note:

1. Zero {0} is also a rational number.

2. All rational numbers are not fractions but all fractions are rational numbers.

Irrational Numbers {Q’}:

The numbers which cannot be written in the form of p/q, q≠0, where p and q are integers are called Irrational numbers. Irrational numbers are denoted by ‘Q’’.

Examples: √2, √3, √5, √6, √7, etc.

Real Numbers {R}:

It is the combination of all of the above numbers i.e. N, W, Z, Q and Q’. Real numbers are denoted by ‘R’.