VARIOUS TYPES OF NUMBERS | IMPORTANT FACTS ABOUT NUMBERS | IMPORTANT FORMULAE:

 VARIOUS TYPES OF NUMBERS: 

• NATURAL NUMBERS :

Counting numbers are called natural numbers. thus, 1,2,3,4,5,....... are all natural numbers. 

• WHOLE NUMBERS:

All natural along with zero are called whole numbers. natural numbers includes zero are terminated as whole numbers. thus, 0,1,2,3,4.............. are the set of whole numbers.

• INTEGERS:

integers includes natural numbers, zero, along with negative form of natural numbers. thus .....-3,-2,-1,0,1,2,3..... are the set of integers. 

set of positive integers = [1,2,3,4,5,6....]

set of negative integers = [-1,-2,-3,-4,.....]

set of all non negative integers are  = [0,1,2,3,4,5,.....]

• EVEN NUMBERS:

A counting number which is divisible by 2 is called as an even numbers. thus,0,1,2,3,4,5...etc are called even numbers. 

• ODD NUMBERS:

A set of counting numbers which are not divided by 2 and getting the final remainder other than 0 are called odd numbers

thus, 1,3,5,7,9,.......etc are called odd numbers

• PRIME NUMBERS:
  

A counting number is called as a prime number if it has exactly two factors, namely itself and 1. 

EX: prime numbers less than 100 are, 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97.

• COMPOSITE NUMBERS:

All composite numbers, without are not prime, are called composite numbers. a composite number has more than two factors.  

• PERFECT NUMBERS:

A number , the sum of whose factors except the number list, is equal to the number , is called a perfect number. e.g 6,28,496.

the factors of 6 are 1,2,3 and 6. and, 1+2+3=6.

the factors of 28 are 1,2,4,7,14 and 28. and, 1+2+4+7+14=28.

• CO-PRIMES PR RELATIVE PRIMES:

Two numbers whose Highest common factor is 1 are called co-prime numbers. EX. (2,3),(8,9) are pairs of co-primes.

• TWIN PRIMES:

Two prime numbers which are having difference 2 are called twin-primes. 

EX. (3,5),(5,7),(11,13) are pairs of twin-primes.

• RATIONAL NUMBERS:

Numbers which can be expressed in the form p/q, where p and q are integers and q not equal to 0, are called rational numbers. 

EX. 1/8,-8/11,0,6,5(2/3) etc.

• IRRATIONAL NUMBERS:

Numbers which can be expressed in decimal form would be in non terminating, and non repeating form, are called irrational numbers. 

EX. 

IMPORTANT FACTS:

• All natural numbers are whole numbers,
• all whole numbers are not natural numbers. 0 is a whole number which is nor a natural number.
• even number+even number= even number
• odd number+odd number=even number
• even number+odd number=odd number
• even number-even number=even number
• odd number-odd number=even number
• even number-odd number=odd number
• odd number-even number=odd number
• even number*even number=even number
• odd number*odd number=odd number
• even number*odd number=even number

IMPORTANT FORMULAE:

1. (a+b)^2 = a^2 + b^2 + 2ab.
2. (a-b)^2 = a^2 + b^2 - 2ab.
3. (a+b)^2 + (a-b)^2 = 2(a^2 + b^2).
4. (a+b)^2 - (a-b)^2 = 4ab.
5. (a+b)^3 = a^3 + b^3 + 3ab(a+b).
6. (a-b)^3 = a^3 - b^3 - 3ab(a-b) a^2 - b^2 = (a + b) (a - b).
7. (a + b + c)^2 = a^2 + b^2 + c^2 + 2( ab + bc + ca ).
8. a^3 + b^3 = (a + b ) ( a^2 + b^2 - ab ) .
9. a^3 - b^3 = ( a - b ) ( a^2 + b^2 + ab ).
10. b^3 + a^3 + c^3 - 3abc = ( a + b + c ) ( a^2 + b^2 + C^2 - ab - bc - ca ).
11. if a + b + c = 0, then a^3 + b^3 + c^3 = 3abc.     

by learning you will be able to do all kind of maths with a basic knowledge. basic maths is much important for future. knowledge cant be wasted.

the content given here is useful for those who are preparing for competetive exams.