Sunday, 11 November 2018

Number system in maths: Definition, Types and Examples

         Number system in maths


Number system comprises various types of numbers. Let us begin by understanding one by one.

Natural Numbers

All the counting numbers are called natural number. 
Example: 1,2,3,4,5,...

  (a) Even Numbers: The numbers which are exactly divisible by 2 are called even numbers. Example: 2,4,6,8,...

  (b) Odd Numbers: The numbers which have a remainder 1 when divided by 2 are called odd numbers. Example: 1,3,5,7,...

  (c) Prime Numbers: If a number is not divisible by any other number except 1 and itself, it is called a prime number. Example: 2,3,5,7,...
       Co-primes: Two numbers which have no common factor between them except 1are said to be co-prime to each other. The two numbers are individually may be prime or composite. Example: 13 and 29 are co-primes.

  (d) Composite Numbers: Numbers which are divisible by other numbers along with 1 and itself are called composite numbers. Example: 4,6,8,9,10,...
N.B: The number 1 is neither prime nor composite.


Whole Numbers

Natural numbers along with '0' form the set of whole numbers.
Example: 0,1,2,3....


Integers

All counting numbers and their negatives along with zero are called Integers.
Example: -4,-3,-2,-1,0,1,2,3,...

Rational and Irrational Numbers

Any number which can be expressed in the form of (p/q), where p and q are integers and q is not equal to '0', is a rational number.
Example: 3/5, 4, -6,...

Numbers which are represented by non-terminating and non-recurring decimals are called irrational numbers. 
Example: 2 = 1.4141...

Real Numbers

The rational and irrational number taken together are called real numbers. The real numbers are the set of numbers containing all of the rational numbers and all of the irrational numbers. The real numbers are "all numbers" on the number line. There are infinitely many real numbers as there are infinitely many numbers in each of the other sets of numbers.

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