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.
Read more about Numeral System: Types, Positional Systems in Detail, Generalized Variable-length Integers
Famous quotes containing the word system:
“Few white citizens are acquainted with blacks other than those projected by the media and the so—called educational system, which is nothing more than a system of rewards and punishments based upon one’s ability to pledge loyalty oaths to Anglo culture. The media and the “educational system” are the prime sources of racism in the United States.”
—Ishmael Reed (b. 1938)