Numeral System

A numeral system (or system of numeration) is a writing system for expressing numbers, that is a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner. It can be seen as the context that allows the symbols "11" to be interpreted as the binary symbol for three, the decimal symbol for eleven, or a symbol for other numbers in different bases.

Ideally, a numeral system will:

• Represent a useful set of numbers (e.g. all integers, or rational numbers)
• Give every number represented a unique representation (or at least a standard representation)
• Reflect the algebraic and arithmetic structure of the numbers.

For example, the usual decimal representation of whole numbers gives every whole number a unique representation as a finite sequence of digits. However, when decimal representation is used for the rational or real numbers, such numbers in general have an infinite number of representations, for example 2.31 can also be written as 2.310, 2.3100000, 2.309999999…, etc., all of which have the same meaning except for some scientific and other contexts where greater precision is implied by a larger number of figures shown.

Numeral systems are sometimes called number systems, but that name is ambiguous, as it could refer to different systems of numbers, such as the system of real numbers, the system of complex numbers, the system of p-adic numbers, etc. Such systems are not the topic of this article.

Other articles related to "numeral system, system, numerals, numeral systems":

Numeral System - Generalized Variable-length Integers
... Unlike a regular based numeral system, there are numbers like 9b where 9 and b each represents 35 yet the representation is unique because ac and aca are not allowed – the a would terminate the number ...
Ternary
... compound Ternary computer, a computer using a ternary numeral system Ternary form, a form used for structuring music Ternary Golay code, a perfect ternary linear code Ternary ...
Hindu–Arabic Numeral System
... The Hindu-Persian numeral system or Hindu numeral system is a positional decimal numeral system developed between the 1st and 5th centuries by Indian mathematicians ... The system was adopted by Persian (Al-Khwarizmi's c. 825 book On the Calculation with Hindu Numerals) and Arab mathematicians (Al-Kindi's c ...
Arithmetik - Decimal Arithmetic
... in common use, to the written numeral system employing arabic numerals as the digits for a radix 10 ("decimal") positional notation however, any numeral system based on powers of 10, e.g ... Greek, Cyrillic, Roman, or Chinese numerals may conceptually be described as "decimal notation" or "decimal representation" ... Arabic world, were introduced into Europe by Fibonacci using the Hindu-Arabic numeral system ...
Positional Notation - Mathematics - Base of The Numeral System
... In mathematical numeral systems, the base or radix is usually the number of unique digits, including zero, that a positional numeral system uses to represent numbers ... For example, for the decimal system the radix is 10, because it uses the 10 digits from 0 through 9 ... The highest symbol of a positional numeral system usually has the value one less than the value of the base of that numeral system ...

Famous quotes containing the word system:

An avant-garde man is like an enemy inside a city he is bent on destroying, against which he rebels; for like any system of government, an established form of expression is also a form of oppression. The avant-garde man is the opponent of an existing system.
Eugène Ionesco (b. 1912)