TOPICS

Introduction

Number Systems

A set of values used to represent different quantities is known as Number system.

A number N is called a natural number, whoose start from 1 to above.
**i.e.** 1,2,3,4,.....n.

A number W is called a whole number, whoose start from 0 to above.
**i.e.** 0,1,2,3,4,.....n.

A number Z is called an integer number, whoose consist of +ve and -ve numbers.
**i.e.** -n...-3,-2,-1,0,1,2,3...n

Integer Numbers are mainly two types:-

1. Positive Integers **i.e.** 1,2,3,4....n

2. Negative Integers **i.e.** -1,-2,-3,-4....-n

A number r is called a rational number, if it can be written in the form ^{p}⁄_{q}, where p and q are integers and q≠0.
**i.e.** 0.3796, 4.1333...,^{4}⁄_{5} etc.

A number s is called an irrational number, if it cannot be written in the form ^{p}⁄_{q}, where p and q are integers and q≠0.
**i.e.** √5 and 4.10100100010000... etc.

A number i is called a comlex number, if it consist of -ve integer numbers in square root.
**i.e.** √-5,√-2 and √-1 etc.

A number R is called a real number, if it consist of rational numbers, natural numbers, whole numbers, integer numbers but not accept of complex numbers(imaginary numbers).
**i.e.** √5,1,2,-4,-2,0.45,1.222...,^{4}⁄_{5} etc.

There are mainly 7 types of Numbers which are following below :-

Numbers which are exactly divisible by 2 are called even numbers.
**i.e.** 2,4,6,.... Sum of first n even numbers = n(n+1).

Numbers which are not exactly divisible by 2 are called odd numbers.
**i.e.** 1,3,5,.... Sum of first n odd numbers = n²

Numbers which are divisible by one and itself only are called prime numbers.
**i.e.** 2,3,5,7,11....etc.

Two numbers are said to be relatively prime if they do not have any common factor other than 1.
**i.e.** (2,5),(3,7),(11,15)....etc.

Two prime numbers which differ by 2 are called twin primes.
**i.e.** (3,5),(5,7),(7,9),(13,15)....etc.

Numbers which are not prime are called composite numbers.
**i.e.** 4,6,9....etc.

A number is said to be a perfect number, if the sum of all its factors excluding itself is equal to the number itself.
**i.e.** 6,28,496,8128....etc. Factors of 6 are 1,2,3 and 6. Sum of factors excluding 6=1+2+3=6. So 6 is a perfect number.

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