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| × | |
|---|---|
Multiplication sign | |
| In Unicode | U+00D7 ×MULTIPLICATION SIGN (×) |
| Different from | |
| Different from | U+0078 xLATIN SMALL LETTER X |
| Related | |
| See also | U+22C5 ⋅DOT OPERATOR U+00F7 ÷DIVISION SIGN |
Themultiplication sign (×), also known as thetimes sign or thedimension sign, is amathematical symbol used to denote the operation ofmultiplication, which results in aproduct.[1]
The symbol is also used inbotany, in botanicalhybrid names.
The form is properly a four-foldrotationally symmetricsaltire.[2] The multiplication sign× is similar to a lowercaseX (x).
The earliest known use of the× symbol to indicate multiplication appears in an anonymous appendix to the 1618 edition ofJohn Napier'sMirifici Logarithmorum Canonis Descriptio.[3] This appendix has been attributed toWilliam Oughtred,[3] who used the same symbol in his 1631 algebra text,Clavis Mathematicae, stating:
Multiplication of species [i.e. unknowns] connects both proposed magnitudes with the symbol 'in' or×: or ordinarily without the symbol if the magnitudes be denoted with one letter.[4]
Other works have been identified in which crossed diagonals appear in diagrams involving multiplied numbers, such asRobert Recorde'sThe Ground of Arts[5][6] andOswald Schreckenfuchs's 1551 edition ofAlmagest, but these are not symbolizations.[3]
Inmathematics, thesymbol × has a number of uses, including
Inbiology, the multiplication sign is used in a botanicalhybrid name, for instanceCeanothus papillosus ×impressus (a hybrid betweenC. papillosus andC. impressus) orCrocosmia × crocosmiiflora (a hybrid between two other species ofCrocosmia). However, the communication of these hybrid names with a Latin letter "x" is common, especially when the actual "×" symbol is not readily available.
The multiplication sign is also used byhistorians for an event between twodates. When employed between two dates – for example 1225 and 1232 – the expression "1225×1232" means "no earlier than 1225 and no later than 1232".[8]
Amonadic× symbol is used by theAPL programming language to denote thesign function.
The lower-case Latin letterx is sometimes used in place of the multiplication sign. This is considered incorrect in mathematical writing.[citation needed]
Inalgebraic notation, widely used in mathematics, a multiplication symbol is usually omitted wherever it would not cause confusion: "a multiplied byb" can be written asab ora b.[1]
Other symbols can also be used to denote multiplication, often to reduce confusion between the multiplication sign × and the common variablex. In some countries, such asGermany, the primary symbol for multiplication is the "dot operator"⋅ (as ina⋅b). This symbol is also used in compoundunits of measurement, e.g., N⋅m (seeInternational System of Units § Lexicographic conventions). In algebra, it is a notation to resolve ambiguity (for instance, "b times2" may be written asb⋅2, to avoid being confused with a value calledb2). This notation is used wherever multiplication should be written explicitly, such as in "ab =a⋅2 forb = 2"; this usage is also seen in English-language texts. In some languages, the use offull stop as a multiplication symbol, such asa.b, is common when the symbol fordecimal point iscomma.
Historically, computer languagesyntax was restricted to theASCII character set, and theasterisk* became the de facto symbol for the multiplication operator. This selection is reflected in thenumeric keypad on English-language keyboards, where the arithmetic operations of addition, subtraction, multiplication and division are represented by the keys+,-,* and/, respectively.
Other variants and related characters:
Multiplicatio speciosa connectit utramque magintudinem propositam cum notâ in vel ×: vel plerumque absque notâ, si magnitudines denotentur unica litera