3. Number theory is one of the oldest branches of pure
mathematics and focusses on the study of natural
numbers.
It is composed of various numbers , symboles or figures
representing numbers and certain rules governing
operation on them. The number can be represented by
{1,2,3,…..},{I,II,III…..} or {k,k*,k**…}.
What is of imfortance is the nature and
characteristic of this number?
4. Number Systems
The Natural Numbers
The number 1,2,3,4…which are used for counting are natural
numbers.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 are the natural numbers together with 0.
The Integers
The Integers are whole numbers ,negetive or zero.We can also
define them as ratios of two numbers which do not have a
remainder.
The set of integers is sometimes written J or Z for short.
5. Types of Number Systems
Real number
A Real number refers to any number that you would
expect to find on the number line.It is a number
whose name will be the “adress” of a point on the
number line.
Real numbers can be classified:
Rational numbers
Irrational numbers
6. Real Numbers
Rational Number
The number which can be expressed in the
form p/q where p is any integer and q is a integer not
equal to zero is called a rational number.
Irrational Numbers
The number which cannot be expressed in the form
p/q where q not equal zero and p,q are both integers,
are called irrational numbers.
7. Number Systems
Imaginary Numbers:
Sqare roots of Negative numbers are called imaginary
numbers because the square of any number is positive
only.
Complex number:
If a and b the real numbers then a+ib is known as a
complex number which has “a” the real part “b”the
imaginary part.
