Number System:

A number system is defined as the system of expressing numbers.

Real Numbers

In a Number System Real numbers are the numbers which include both Rational and Irrational numbers.

Natural Numbers:-

In a Number System all counting numbers 1,2,3,4…are called Natural numbers. If N is the set of natural numbers, then N = {1, 2, 3, 4,…}.

Whole Numbers:

In a Number System all the natural numbers including 0 form the set of whole numbers. It is denoted by W. Thus W = {0,1,2,3,4,…}

Irrational Numbers:

An Irrational Number is a real number that cannot be written as a simple fraction. Irrational means not Rational.

Composite Numbers :-

• A natural number “a“is said to be Composite if it has at least one more divisor except 1 and ‘a’ itself.

• For example 4,6,8,9,10,12,14,…are all composite numbers.

Integers:-

• In a Number System all the natural numbers, their negatives and zero form the set of integers.

• It is denoted by Z. Thus Z = {0,± 1, ±2,±3, ±4,…}.

• Integers are also denoted by I.

Rational numbers:-

• A number in the form of p/q where p and q are integers; and i,e are co-primes is called a rational number.

• Rational numbers are denoted by Q (Q comes from word Quotient).

• Note:-The word ‘Rational’ is derived from the word ‘ratio’.

Twin Primes:-

• A pair of prime numbers is said to be Twin Primes if they differ by 2.

• For example 3,5; 5,7; 11,13; 17,19 are Twin Primes while as 7,11; 13,17 are not Twin Primes.

Co-prime:-

Two numbers are said to be co-prime or relatively prime if their Highest Common Factor or Greatest Common Divisor is 1.