Multiplication sign
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× | |
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Multiplication sign | |
In Unicode | U+00D7 × MULTIPLICATION SIGN (×) |
Different from | |
Different from | U+0078 x LATIN SMALL LETTER X |
Related | |
See also | U+22C5 ⋅ DOT OPERATOR U+00F7 ÷ DIVISION SIGN |
The multiplication sign (×), also known as the times sign or the dimension sign, is a mathematical symbol used to denote the operation of multiplication, which results in a product.[1] While similar to a lowercase X (x), the form is properly a four-fold rotationally symmetric saltire.[2]
The symbol is also used in
History
The earliest known use of the × symbol to represent multiplication appears in an anonymous appendix to the 1618 edition of John Napier's Mirifici Logarithmorum Canonis Descriptio.[3] This appendix has been attributed to William 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]
Two earlier uses of a ✕ notation have been identified, but do not stand critical examination.[3]
Uses
In mathematics, the symbol × has a number of uses, including
- numbers, where it is read as "times" or "multiplied by"[1]
- Cross product of two vectors, where it is usually read as "cross"
- Cartesian product of two sets, where it is usually read as "cross"[5]
- Geometric dimension of an object, such as noting that a room is 10 feet × 12 feet in area, where it is usually read as "by" (e.g., "10 feet by 12 feet")
- Screen resolutionin pixels, such as 1920 pixels across × 1080 pixels down. Read as "by".
- Dimensions of a matrix, where it is usually read as "by"
- A statistical interaction between two explanatory variables, where it is usually read as "by"
In
The multiplication sign is also used by historians for an event between two dates. When employed between two dates – for example 1225 and 1232 – the expression "1225×1232" means "no earlier than 1225 and no later than 1232".[6]
A monadic × symbol is used by the APL programming language to denote the sign function.
Similar notations
The lower-case Latin letter x is sometimes used in place of the multiplication sign. This is considered incorrect in mathematical writing.
In algebraic notation, widely used in mathematics, a multiplication symbol is usually omitted wherever it would not cause confusion: "a multiplied by b" can be written as ab or a b.[1]
Other symbols can also be used to denote multiplication, often to reduce confusion between the multiplication sign × and the common variable x. In some countries, such as
Historically, computer language
Typing the character
SGML, XML
|
× or ×
|
macOS | In the Character Palette by searching for MULTIPLICATION SIGN[7] |
Microsoft Windows |
|
OpenOffice.org | times |
TeX |
|
Unix-like (Linux, ChromeOS) |
|
Unicode and HTML entities
- U+00D7 × MULTIPLICATION SIGN (×)
Other variants and related characters:
- U+002A * ASTERISK (*, *)
- U+2062 INVISIBLE TIMES (⁢, ⁢) (a zero-width space indicating multiplication)
- U+00B7 · MIDDLE DOT (·, ·, ·) (the interpunct, may be easier to type than the dot operator)
- U+2297 ⊗ CIRCLED TIMES (⊗, ⊗)
- U+22C5 ⋅ DOT OPERATOR (⋅)
- U+2715 ✕ MULTIPLICATION X
- U+2716 ✖ HEAVY MULTIPLICATION X
- U+2A09 ⨉ N-ARY TIMES OPERATOR
- U+2A2F ⨯ VECTOR OR CROSS PRODUCT (⨯) (intended to explicitly denote the cross product of two vectors)
- U+2A30 ⨰ MULTIPLICATION SIGN WITH DOT ABOVE (⨰)
- U+2A31 ⨱ MULTIPLICATION SIGN WITH UNDERBAR (⨱)
- U+2A34 ⨴ MULTIPLICATION SIGN IN LEFT HALF CIRCLE (⨴)
- U+2A35 ⨵ MULTIPLICATION SIGN IN RIGHT HALF CIRCLE (⨵)
- U+2A36 ⨶ CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENT (⨶)
- U+2A37 ⨷ MULTIPLICATION SIGN IN DOUBLE CIRCLE (⨷)
- U+2A3B ⨻ MULTIPLICATION SIGN IN TRIANGLE (⨻)
- U+2AC1 ⫁ SUBSET WITH MULTIPLICATION SIGN BELOW (⫁)
- U+2AC2 ⫂ SUPERSET WITH MULTIPLICATION SIGN BELOW (⫂)
See also
- Division sign
- List of mathematical symbols
- Plus and minus signs
- Reference mark
- X mark
References
- ^ a b c Weisstein, Eric W. "Multiplication". mathworld.wolfram.com. Retrieved 2020-08-26.
- ISSN 0036-6803.
- ^ a b c Cajori, Florian (1928). A History of Mathematical Notations, Volume I: Notations in Elementary Mathematics. Open Court. pp. 251–252.
- ^ William Oughtred (1667). Clavis Mathematicae. p. 10.
Multiplicatio speciosa connectit utramque magintudinem propositam cum notâ in vel ×: vel plerumque absque notâ, si magnitudines denotentur unica litera
- ^ Nykamp, Duane. "Cartesian product definition". Math Insight. Retrieved August 26, 2020.
- ISBN 978-0-19-861041-0
- ^ "Mac Zeichenpalette" (in German). TypoWiki. Archived from the original on 2007-10-25. Retrieved 2009-10-09.
- ^ "Unicode Character 'MULTIPLICATION SIGN' (U+00D7)". Fileformat.info. Retrieved 2017-01-13.
External links
- "Letter Database". Eki.ee. Retrieved 2017-01-13.
- "Unicode Character 'MULTIPLICATION SIGN' (U+00D7)". Fileformat.info. Retrieved 2017-01-13.
- "Unicode Character 'VECTOR OR CROSS PRODUCT' (U+2A2F)". Fileformat.info. Retrieved 2017-01-13.