Number System

R = Real Numbers:

All rational and irrational numbers are called real numbers.

I = Integers:

All numbers from (…-3, -2, -1, 0, 1, 2, 3…) are called integers.

Q = Rational Numbers:

Real numbers of the form p/q , q ≠ 0, p, q ∈ I are rational numbers.

Q’ = Irrational Numbers:

Real numbers which cannot be expressed in the form p/q and whose decimal expansions are non-terminating and non-recurring.

Roots of primes like √2, √3, √5 etc. are irrational

N = Natural Numbers:

Counting numbers are called natural numbers. N = {1, 2, 3, …}

W = Whole Numbers:

Zero along with all natural numbers are together called whole numbers. {0, 1, 2, 3,…}

Even Numbers:

Natural numbers of the form 2n are called even numbers. (2, 4, 6, …}

Even numbers are divisible by 2.

Odd Numbers:

Natural numbers of the form 2n -1 are called odd numbers. {1, 3, 5, …}

Odd numbers are not divisible by 2.

Prime Numbers:

The natural numbers greater than 1 which are divisible by 1 and the number itself are called prime numbers, Prime numbers have two factors i.e., 1 and the number itself For example, 2, 3, 5, 7 & 11 etc.

Composite Numbers:

The natural numbers which are divisible by 1, itself and any other number or numbers are called composite numbers. For example, 4, 6, 8, 9, 10 etc.

Note:

1 is neither prime nor a composite number.

All Natural Numbers are whole numbers.

All Whole Numbers are Integers.

All Integers are Rational Numbers.

All Rational Numbers are Real Numbers.