# Chapter 1 Number Systems Exercise 1.1 Introduction

Natural Numbers The counting numbers are known as natural numbers. The collection of all natural numbers is denoted by ‘N’

N = { 1, 2, 3, 4 ………………….. ∞ }

Whole Numbers If 0 is included in the collection of natural numbers then the collection 0,1,2,3,4…..infinite are known as whole numbers and it is denoted by ‘W’

W = { 0, 1, 2, 3, 4 ………………….. ∞ }

Integers The collection of natural numbers, zero and their negative numbers are known as Integers or we can say collection of negative numbers and whole numbers are known as integers which is denoted by ‘Z’

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

Rational Numbers Numbers are of the form p/q, where q ≠ 0 and p & q are integers are known as rational numbers and it is denoted by ‘Q’

Q = { p/q  ; where q ≠ 0 ;  p, q ∈ Z }

Irrational Numbers Numbers which can not be written in the form of p/q where q ≠ 0 and p, q are integers are known as irrational numbers.

√2, √3, π etc

Real Numbers The collection of all rational numbers and irrational numbers together is called real number which is denoted by ‘R

R = Rational numbers + Irrational numbers