There are many different

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. The same sequence of symb ...

s, that is,

writing system A writing system is a method of visually representing verbal communication, based on a script and a set of rules regulating its use. While both writing and speech are useful in conveying messages, writing differs in also being a reliable for ...

s for expressing numbers.

By culture / time period

By type of notation

Numeral systems are classified here as to whether they use positional notation (also known as place-value notation), and further categorized by radix or base.

Standard positional numeral systems

The common names are derived somewhat arbitrarily from a mix of

Latin Latin (, or , ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through the power ...

and

Greek Greek may refer to: Greece Anything of, from, or related to Greece, a country in Southern Europe: *Greeks, an ethnic group. *Greek language, a branch of the Indo-European language family. **Proto-Greek language, the assumed last common ancestor ...

, in some cases including roots from both languages within a single name. There have been some proposals for standardisation.

Non-standard positional numeral systems

Bijective numeration

Signed-digit representation

Negative bases

The common names of the negative base numeral systems are formed using the prefix ''nega-'', giving names such as:

Complex bases

Non-integer bases

''n''-adic number

Mixed radix

Factorial number system In combinatorics, the factorial number system, also called factoradic, is a mixed radix numeral system adapted to numbering permutations. It is also called factorial base, although factorials do not function as base, but as place value of di ...

* Even double factorial number system * Odd double factorial number system * Primorial number system *

Fibonorial In mathematics, the Fibonorial , also called the Fibonacci factorial, where is a nonnegative integer, is defined as the product of the first positive Fibonacci numbers, i.e. : _F := \prod_^n F_i,\quad n \ge 0, where is the th Fibonacci number, ...

number system * in timekeeping * in timekeeping * (12, 20) traditional English monetary system (£sd) * (20, 18, 13) Maya timekeeping

Other

* Quote notation * Redundant binary representation * Hereditary base-n notation * Asymmetric numeral systems optimized for non-uniform probability distribution of symbols * Combinatorial number system

Non-positional notation

All known numeral systems developed before the Babylonian numerals are non-positional,Chrisomalis calls the Babylonian system "the first positional system ever" in . as are many developed later, such as the Roman numerals. The French Cistercian monks created their own numeral system.

References