Subtractive notation

Subtractive notation

Subtractive notation is an early form of positional notation used with Roman numerals as a shorthand to replace four or five characters in a numeral representing a number with usually just two characters. Using subtractive notation the numeral VIIII becomes simply IX. LXXXXVIII would become IIC, which is invalid in Roman numerals though.

Without subtractive notation, XIV represents the same number as XVI (16 in Arabic numerals). With the introduction of subtractive notation, XIV (14) no longer represents the same number as XVI but rather is an alternate way of writing XIIII.

By encoding information about the number into the order of the numerals, subtractive notation transformed the Roman numeral system from a variation of a unary numeral system which used alphabetic characters to represent groupings of tally marks (a position-independent counting system). This form of notation closely follows Latin language usage, in which the number 18 is pronounced as "duodeviginti", meaning "two [deducted] from twenty" ("duo-de-viginti"), and 19 is pronounced "undeviginti", meaning "one [deducted] from twenty" ("un-de-viginti").

While simplifying the presentation of numerals, subtractive notation removed from Roman arithmetic the advantages of a tally system for speedy addition and subtraction without adding the flexibility of later positional notations systems for mathematics.

The very positive advantage of subtractive notation is the reduction of counters needed on a abacus, the calculating devices used by the Romans, and those before them for thousands of years. They did not do arithmetic with their written numerals. They used their numerals only for recording the results of calculations on an abacus. Reduction of counters is also why they used intermediate 5 values, i.e. V, L, and D. The number of counters needed to represent IIIIIIIII, VIIII, and IX are 9, 5, and 2. Subtractive notation reflected the counter positions on an abacus with positive and negative counters on opposite sides of a median line.


Wikimedia Foundation. 2010.

Игры ⚽ Нужно сделать НИР?

Look at other dictionaries:

  • Notation SMILES — Simplified Molecular Input Line Entry Specification Le Simplified Molecular Input Line Entry Specification ou SMILES est un langage symbolique de description de la structure des molécules chimiques sous forme de courtes chaînes de caractères… …   Wikipédia en Français

  • Positional notation — Numeral systems by culture Hindu Arabic numerals Western Arabic (Hindu numerals) Eastern Arabic Indian family Tamil Burmese Khmer Lao Mongolian Thai East Asian numerals Chinese Japanese Suzhou Korean Vietnamese …   Wikipedia

  • Roman numerals — are a numeral system originating in ancient Rome, adapted from Etruscan numerals. The system used in classical antiquity was slightly modified in the Middle Ages to produce a system used today. It is based on certain letters which are given… …   Wikipedia

  • Roman arithmetic — In mathematics, Roman arithmetic is the use of arithmetical operations on Roman numerals.In modern education, Roman arithmetic is seldom taught. The preferred method is to convert the Roman numeral into an Arabic numeral system and solve the… …   Wikipedia

  • Numeral system — This article is about different methods of expressing numbers with symbols. For classifying numbers in mathematics, see number system. For how numbers are expressed using words, see number names. Numeral systems by culture Hindu Arabic numerals… …   Wikipedia

  • List of mathematics articles (S) — NOTOC S S duality S matrix S plane S transform S unit S.O.S. Mathematics SA subgroup Saccheri quadrilateral Sacks spiral Sacred geometry Saddle node bifurcation Saddle point Saddle surface Sadleirian Professor of Pure Mathematics Safe prime Safe… …   Wikipedia

  • St Edmund Hall, Oxford — Oxford College Infobox primary colour = #801213 name = St Edmund Hall name Latin = Aula Sancti Edmundi university = Oxford picture = shield = colours = cell|#801213cell|#801213cell|#801213cell|#F0DC82cell|#801213cell|#801213cell|#801213cell|#F0DC8… …   Wikipedia

  • numerals and numeral systems — ▪ mathematics Introduction       a collection of symbols used to represent small numbers, together with a system of rules for representing larger numbers.       Just as the first attempts at writing came long after the development of speech, so… …   Universalium

  • photography, technology of — Introduction       equipment, techniques, and processes used in the production of photographs.  The most widely used photographic process is the black and white negative–positive system (Figure 1 >). In the camera the lens projects an image of… …   Universalium

  • HSL and HSV — Fig. 1. HSL (a–d) and HSV (e–h). Above (a, e): cut away 3D models of each. Below: two dimensional plots showing two of a model’s three parameters at once, holding the other constant: cylindrical shells (b, f) of constant saturation, in this case… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”