A number is a mathematical object that is used to count something. The mathematical numbers are used to measure some quantity or to count some substance or material. Mathematical numbers are classified into different classes such as natural numbers, whole numbers, odd numbers, and, even numbers. Given below are some basic concepts regarding numbers.

Natural numbers

Numbers 1, 2, 3, 4, … Are known as natural numbers.

Set of natural numbers

N = {1, 2, 3, 4, … }

Whole numbers

Numbers 0, 1, 2, 3, 4, … are known as whole numbers

Set of whole numbers

W = {0, 1, 2, 3, 4, …}

Integers

All counting numbers including negatives and zero are known as integers

Set of integers

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

Rational number

A number of the form p/q, where p and q are integers, are known as rational numbers, where q ≠ 0.

Set of rational numbers

Q = { x: x = p/q, p,q ∈ I, q ≠ 0 }

Irrational numbers

Rational numbers are those numbers when expressed in decimal form are neither terminating nor repeating are known as irrational numbers.

Even numbers

The numbers which are exactly divisible by 2 are known as even numbers.

Odd numbers

All numbers which are not exactly divisible by 2 are known as odd numbers.

Prime numbers

A natural number (other than 1) which is divisible by 1 and by itself only.

Composite numbers

Natural numbers (excluding 1) which are not prime are known as composite numbers.

Good to know

NamePowerNumber
Million1061,000,000
Billion1091,000,000,000
Trillion10121,000,000,000,000
Quadrillion1015 1,000,000,000,000,000