development of number systems with their needs
Answers
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
a.(b+c)=a.b+a.c