# Number system

The number system is the system or structure of representing numbers. Any numerous sets of numbers which are symbols and have rules for using them to denote a series of numbers and thus to list how many numbers are there in a given set of the number system.

Number systems are present from Mesopotamian age and are the symbols that represent different values. The emblem of roman numeral I, alpha, and the digit one all represent the idea of oneness and are the starting symbol of these number systems. The present number system that is followed is place-value systems. In Place-value systems, the value of the numbers depends on the position of the digits in the name. For example, 3, 30, and 300; here 3 represents different values due to the arrangement and positioning of 3 and 0s.

The decimal positioning system is the other most used number system. In the Decimal positioning system, all ten numbers from 0-9 are used to construct all required numbers. Indians discovered the decimal positioning system.

The simplest number system is a Unary number system. In the Unary number system, every natural number is represented by symbol /. For example the number 5 will be represented by ///// i.e 5/. Here / stands for one, * stands for ten and – for 100. This system is used in computer science programming.

The two number systems which are used in computer science and computer coding are Binary Number system and Hexadecimal system. The Binary number system includes two digits as its base. The two digits are 0s and 1s. Different combinations of 0 and 1 are used to form different numbers, each representing a different value. For example, 100110, 010110, 101010111 are some characters in the Binary number system. The Hexa-decimal system includes 16 characters and hence the base 16. The first 10 are the digits 0-9 and then six alphabets from a-f. These characters make up the hexadecimal system.

The natural numbers system is also known as the counting numbers, and the series starts from 1. Natural numbers are infinite. The whole numbers are similar to natural numbers, but they start at 0. Whole numbers include natural numbers. Thus natural numbers are a subset of whole numbers. Whole numbers are also infinite.

The integers are the set of number systems, which includes a set of real numbers, their additive inverse, and zero. Thus integers are {…-3,-2,-1,0,1,2,3….}. The integers are represented by Z. Integers can be represented on number line also.

The rational numbers are the ones that can be represented by a ratio between two integers. For example, fractions 15 and -1130 are both rational numbers. All the fractions which terminate or have a recurrent pattern are both rational numbers.

An irrational number is a number that cannot be represented as a fraction. The irrational numbers do not end in decimal form. Pi is an irrational number.

Real numbers are the set of numbers that contain all rational and irrational numbers. The real numbers contain all the numbers and are infinite.

These were some of the important numbers of systems.

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