 # Number System PDF

Number system can be defined as the collection of numbers. Below are the types of the number system.

## Classification of Number System (PDF)

The natural numbers are classified as follows:

### Natural Numbers

Natural numbers or counting numbers starting from 1, 2, 3, …. are the most familiar numbers. They are symbolically represented by N. Natural numbers together with 0 are called whole numbers. Interesting fact:

Sum of two natural numbers is a natural number. Also, the product of two natural numbers is a natural number.

### Integers

Natural numbers are a subset of integers. Natural numbers without zero are called positive integers, and when written with a negative sign are called as negative integers. The set of integers is represented by the symbol Z.

### Rational Numbers

• A fraction with an integer numerator and a positive integer in the denominator. It is represented in the form of p / q where p and q are integers and q is not equal to zero
• Decimal numbers which have a repeating pattern will also fall under this category. Example: 0.083333…. = 1 / 12
• All integers are rational numbers

### Irrational Numbers

• A number that cannot be written as a fraction, i.e. p / q.
• It is a never-ending number and does not repeat itself in the decimal form. Example: π = 3.14159…
• This was first discovered by the Pythagorean in Greece.

### Real Numbers

• The set of all the rational and irrational numbers are called real numbers
• Represented by the symbol R

### Prime Numbers

• Any real number that is divisible by 1 and itself come under this category
• Example of prime numbers 2, 3, 5, 7, 11…

Further classification of the number system is as follows.

• Decimal
• Binary
• Octal