This document defines and explains various number systems including: - Natural numbers which are 1, 2, 3, etc. - Whole numbers which are the natural numbers and 0. - Integers which are whole numbers and their opposites. - Rational numbers which are fractions with integer numerators and denominators. - Irrational numbers which cannot be written as fractions. - Real numbers which are all rational and irrational numbers on the number line. - Complex numbers which are numbers expressed as a + bi, where a and b are real numbers and i is the imaginary unit.

2. NUMBER SYSTEMTOPIC :
MELVE FRANCIS
B.Ed,Mathematics
Mangalam College of
Education

3. NUMBER SYSTEM
• Natural numbers
• Whole numbers
• Integers
• Rational number
• Irrational number
• Real numbers
• Interval
• Complex number

4.  The Natural Numbers
The natural (or 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.
 The whole numbers
The whole numbers are the natural
numbers together with 0.

5.  The Integers
The integers are the set of real numbers consisting of the natural
numbers, their additive inverses and zero.
{...,−5,−4,−3,−2,−1,0,1,2,3,4,5,...}
The set of integers is sometimes written J or Z for short.
The sum, product, and difference of any two integers is also an integer. But this is not
true for division.

6.  The Rational Number
A rational number is a fraction a/b,
where a is an integer and b is an integer other than zero.
 The Irrational Number
Irrational number, on the other hand, cannot be written as a
fraction with an integer numerator and denominator.
Examples of irrational numbers include √2 and π.
Rational numbers and irrational numbers are mutually exclusive:
they have no numbers in common.

7.  The Real Numbers
The real numbers is the set of numbers
containing all of the rational numbers and
all of the irrational numbers.
The real numbers are “all the numbers”
on the number line.
 Prime numbers
The real number which is divisible
by 1 and itself is called prime number.

8.  An open interval (a, b) is the set of all real numbers x such
that a < x < b.
 A closed interval [a, b] is the set of all real numbers x such
that a ≤ x ≤ b.
 Interval
An Interval can be defined as the totality of points on a line
between two designated points or end points that may or may not be
included.
)(
(0,3)
0 3
[0,3]
0 3
][

9.  The Complex Number
A complex number is a number that
can be expressed in the form a + bi,
where a and b are real numbers, and i is
the imaginary unit, which satisfies the
equation i2 = −1.
In this expression, a is called the
real part of the complex number, and
b is called the imaginary part.
The symbol for the complex
numbers is C.

10. • 0 - Whole, Integers, Rational, and Real
• 4 - Natural, Whole, Integer, Rational, Real
• -9 - Integer, Rational, Real
• Π - Irrational, Real
• 3/4 or 0.75 - Rational and Real
• 4 - Natural, Whole, Integer, Rational, Real
• 15 - Irrational, Real
 Examples

11. NUMBER SYSTEM