The Number System

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The ten symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 are called digits, which can represent any number.

Natural Numbers:

These are the numbers (1, 2, 3, etc.) that are used for counting. It is denoted by N. There are infinite natural numbers and the smallest natural number is one (1).

Even numbers:

Natural numbers which are divisible by 2 are even numbers. It is denoted by E. For example, E = 2, 4, 6, 8, … The smallest even number is 2. There is no largest even number.

Odd numbers: Natural numbers which are not divisible by 2 are odd numbers. It is denoted by O. For example, O = 1, 3, 5, 7, …. The smallest odd number is 1. There is no largest odd number.

Based on divisibility, there could be two types of natural numbers:

Prime and Composite

  1. Prime Numbers: Natural numbers which have exactly two factors, i.e., 1 and the number itself are called prime numbers. The lowest prime number is 2. 2 is also the only even prime number.

  2. Composite Numbers: It is a natural number that has at least one divisor different from unity and itself.

Every composite number can be factorized into its prime factors.

For example: 24 = 2 × 2 × 2 × 3. Hence, 24 is a composite number.

The smallest composite number is 4.

Whole Numbers:

The natural numbers along with zero (0), from the system of whole numbers. It is denoted by W. There is no largest whole number and The smallest whole number is 0.

Integers:

The number system consisting of natural numbers, their negative and zero is called integers. It is denoted by Z or I. The smallest and the largest integers cannot be determined.

Real Numbers:

All numbers that can be represented on the number line are called real numbers. It is denoted by R.

R+: Positive real numbers and R : Negative real numbers.

Real numbers = Rational numbers + Irrational numbers.

  1. Rational numbers: Any number that can be put in the form of , where p and q are integers and q 0, is called a rational number. It is denoted by Q. Every integer is a rational number. Zero (0) is also a  rational number. The smallest and largest rational numbers cannot be determined. Every fraction (and decimal fraction) is a rational number

2. Irrational numbers: The numbers which are not rational or which cannot be put in the form of , where p and q are integers and q 0, is called irrational number. It is denoted by Q’ or Qc.