Numbers

Natural numbers N = {1, 2, 3, 4...........+∞}

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

Positive integers Z⁺ ={1, 2, 3, 4, ..........+∞}

Negative integers Z^- ={-∞,..........-3, -2, -1}

Non - negative integers or Whole numbers = {0, 1, 2, 3, 4, ..........+∞}

Non - positive integers ={-∞,..........-3, -2, -1,0}

Rational numbers Q

All the numbers of the form p/q, where p an q are integers and b ≠ 0 are called rational numbers and their set is denoted by Q.

i.e. Q=p/q such that a, b ε Z and b≠0 and HCF of a,b is 1.

1. Every integer is a rational number as it could be written as Q=p/q

2. All recurring decimals are rational numbers e.g. Q= 1/3= 0.333333.

Irrational numbers Q^c

Those values which neither terminate nor could be expressed as recurring decimals are called irrational numbers i.e. it cannot be expressed as p/q form, and are denoted by Q^c

e.g. = 1.41421356237309.... , 1+ , -3/ ,

= 3.14159253.....

Real numbers R

The set which contain both rational and irrational are called real numbers and is denoted by R

R={ ,..............-2, -1, 0, 1, 2, 3, ......13/5, .....16/3.......+ }