### Number System

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## Number System

Natural Number

Counting numbers are 1, 2, 3, 4, 5, etc. There are infinitely many natural numbers. The set of natural numbers, 1, 2, 3, 4, 5, ... is sometimes written N for short.

N = {1, 2, 3, 4, 5, ...}

Whole Number

The whole numbers are the natural numbers together with 0.

Every natural number is a whole number but 0 is a whole number which is not a natural number.

Every natural number is a whole number but 0 is a whole number which is not a natural number.

W = {0 ,1, 2, 3, 4, 5, ...}

Integers

The integers are the set of real numbers consisting of the natural numbers, their additive inverses and zero.

Z = {..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5...}

Rational Numbers (Q)

A Rational Number is a real number that can be written as a simple fraction.

Q = {p/q where p,q are integers}

Irrational Numbers (Q)

An Irrational Number is a real number that can not be written as a simple fraction.

Prime Numbers

A number greater than 1 having exactly two factors, namely 1 and itself is called a prime number.

{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61...}

Composite Numbers

A number greater than 1 having more than two factors, namely 1 and itself is called a composite number.

{4, 6, 8, 9, 10, 12, 14, 15, 16...}

Co-prime Numbers

Two natural numbers a and b are said to be co-prime if their HCF is 1.

(5, 7), (4, 5), (2, 3),...