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.

Symbols and numerals

A numeral system allows the symbols "11" to be interpreted as:

• The binary symbol for three
• The decimal symbol for eleven
• A symbol for other numbers in different bases

Value

The number the numeral represents is called its value.

Principles

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 non zero whole number a unique representation as a finite sequence of digits, beginning by a non-zero digit.

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.

Number systems (ambiguous)

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

Such systems are, however, not the topic of this article.

See also

• Binary number
• Digit
• Glyph
• Hexadecimal
• Mathematical notation
• Mathematics
• Natural number
• Number
• Numerical digit
• Positional notation
• Radix
• Rational number
• Real number
• Symbol
• Whole number

External links

• Numeral system @ Wikipedia