Number system can be defined as the collection of numbers. Below are the types of number systems:
- 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.
Sum of two natural numbers is a natural number. Also, product of two natural numbers is a natural number.
Natural numbers are the 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 after some point also fall under this category. Example: 0.083333…. = 1 / 12
- All integers are rational numbers
- Irrational numbers:
- A number that cannot be written as 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 1,2,3,5,7,11…
Further classification of number system is as follows
To learn more about their types and classification download the Number system pdf