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History: The mathematical notation which is used to represent the numbers of a given set is known as number system. It represents the meaningful set of numbers that includes integers and rational numbers. In ancient times, these number system was used like, 1 2 3 which is nowadays known as decimal number system.

Types of number system:

1. Natural numbers:
 1, 2, 3

2. Integers:
0, -1, -2

3. Rational numbers:
In fractions p/q

4. Real numbers:
All the numbers are real numbers.

5. Complex numbers:
The numbers in the form of  z = a + bi, where a and b are real numbers.

6. Algebraic numbers:
The complex numbers.  

Properties of numbers:

1. Associative property
Addition: a+(b+c)=(a+b)+c
Multiplication: a.(b+c)=(a.b).c

2.  Commutative property

Addition: a+b=b+a
Multiplication: a.b=b.a

3. Inverse property
Addition: a+(-a)=0
Multiplication: a.(1/a)=1

4. Distributive property
2 4 2