Subtractive notation

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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 IIII becomes simply IV, while LXXXXVIII becomes IIC.

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 With the introduction of subtractive notation, XIV (14) no longer represents the same number as XVI but rather is an alternate way of writing XIIII.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.