The document defines different types of number systems: natural numbers consist of positive whole numbers starting from 1; whole numbers include 0 and natural numbers as W; integers Z or I are whole numbers and their negatives; rational numbers Q can be expressed as fractions p/q where p and q are integers; irrational numbers cannot be expressed as terminating or repeating decimals and are not rational; and real numbers R are the union of rational and irrational numbers, including both positive and negative numbers.

1. NUMBER SYSTEM
By
RAM SIR

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

5. Numbers from 0 (zero)
onward are known
as Whole numbers,
denoted by ‘W’
W = {0, 1, 2, 3, 4, ......}

6. The collection of all whole numbers and
negative of natural numbers are called
Integers, Denoted by ‘Z’ or ‘I’.
Z or I = {...... –3, –2, –1,0,1,2,3 ......}

7. A number which can be
expressed as where q ≠ 0
and q εZ is know as rational
number, denoted by ‘Q’.

8. A number which can’t be
expressed in the form of p/q and
its decimal representation is
non-terminating and non-repeating
is known as irrational number.
The numbers which are not rational
numbers, are called irrational numbers.

9. Real numbers can be defined as the union of both the
rational and irrational numbers. They can be both
positive or negative and are denoted by the
symbol “R”. All the natural numbers, decimals,
and fractions come under this category..

11. .