Multiplication sign

×
Multiplication sign
Punctuation
apostrophe  '
brackets [ ]  ( )  { }  ⟨ ⟩
colon :
comma ,  ،
dash ‒  –  —  ―
ellipsis  ...
exclamation mark !
full stop, period .
guillemets ‹ ›  « »
hyphen
hyphen-minus -
question mark ?
quotation marks ‘ ’  “ ”  ' '  " "
semicolon ;
slash, stroke, solidus /
Word dividers
interpunct ·
space
General typography
ampersand &
asterisk *
at sign @
backslash \
basis point
bullet
caret ^
dagger † ‡ ⹋
degree °
ditto mark
equals sign =
inverted exclamation mark ¡
inverted question mark ¿
komejirushi, kome, reference mark
multiplication sign ×
number sign, pound, hash #
numero sign
obelus ÷
ordinal indicator º ª
percent, per mil % ‰
plus, minus + −
plus-minus, minus-plus ± ∓
pilcrow
prime
section sign §
tilde ~
underscore, understrike _
vertical bar, pipe, broken bar |    ¦
Intellectual property
copyleft 🄯
service mark
Currency
currency sign ¤

؋฿¢\$֏ƒ£元 圆 圓 ¥ 円

Uncommon typography
asterism
fleuron, hedera
index, fist
interrobang
irony punctuation
lozenge
tie
Related
In other scripts
The multiplication sign

The multiplication sign, also known as the times sign or the dimension sign, is the symbol ×. While similar to the lowercase letter x, the form is properly a rotationally symmetric saltire.[1]

Uses

In mathematics, the symbol × has a number of uses, including

• Multiplication of two scalar numbers, where it is read as "times" or "multiplied by"
• Cross product of two vectors, where it is usually read as "cross"
• Cartesian product of two sets, where it is usually read as "cross"
• 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" (for example: "10 feet by 12 feet")
• 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 biology, the multiplication sign is used in a botanical hybrid name, for instance Ceanothus papillosus × impressus (a hybrid between C. papillosus and C. impressus) or Crocosmia × crocosmiiflora (a hybrid between two other species of Crocosmia). However, the communication of these hybrid names with a standard non-multiplication "x" is common when the actual "×" symbol is not readily available.

The multiplication sign is also used by historians for an event between two dates. When employed between two dates, for example 1225 and 1232, 1225×1232 means "no earlier than 1225 and no later than 1232". It can also be used in a date range: 1225×1232–1278.[2]

History

The multiplication sign (×), often attributed to William Oughtred (who first used it in an appendix to the 1618 edition of John Napier's Mirifici Logarithmorum Canonis Descriptio), apparently had been in occasional use since the mid 16th century.[3]

Similar notations

The 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.

Other symbols can also be used to denote multiplication, often to reduce confusion between the multiplication sign × and the commonly used variable x. In many non-Anglophone countries, rather than ×, the primary symbol for multiplication is U+22C5 dot operator, for which the interpunct · may be substituted as a more accessible character. This symbol is also used in mathematics wherever multiplication should be written explicitly, such as in "ab = a⋅2 for b = 2"; this usage is also seen in English-language texts. In some languages (especially Bulgarian[citation needed] and French[citation needed]) the use of full stop as a multiplication symbol, such as a.b, is common.

Historically, computer language syntax was restricted to the ASCII character set; in the absence of the × character, U+002A * Asterisk became the de facto standard notation of the multiplication operator in computing. This selection is still reflected in the standard numeric keypad, where the arithmetic operations of addition, subtraction, multiplication, and division are represented by the +, -, *, and / keys, respectively.

In computer software

The × symbol is listed in the Latin-1 Supplement character set and is U+00D7 × MULTIPLICATION SIGN (HTML &#215; · &times;) in Unicode. It can be invoked in various operating systems as per the table below.

A monadic × symbol is used by the APL programming language to denote the sign function.

There is a similar character ⨯ at U+2A2F, but this is not always considered identical to U+00D7, as U+2A2F is intended to explicitly denote the cross product of two vectors.

 Mac OS X in Character Palette, search for MULTIPLICATION SIGN[4][5] HTML, SGML, XML × and × Microsoft Windows Alt Gr++ Alt+0215 Alt+0D7[6] Unix-like Ctrl+⇧ Shift+U00D7 Compose X X OpenOffice.org times TeX \times Unicode U+00D7

Unicode

• In Unicode, the basic character is U+00D7 × MULTIPLICATION SIGN (HTML &#215; · &times;)

Other variants are encoded:

• U+2297 CIRCLED TIMES (HTML &#8855; · &otimes;)
• U+2715 MULTIPLICATION X (HTML &#10005;)
• U+2716 HEAVY MULTIPLICATION X (HTML &#10006;)
• U+2A09 N-ARY TIMES OPERATOR (HTML &#10761;)
• U+2A2F VECTOR OR CROSS PRODUCT (HTML &#10799;)
• U+2A30 MULTIPLICATION SIGN WITH DOT ABOVE (HTML &#10800;)
• U+2A31 MULTIPLICATION SIGN WITH UNDERBAR (HTML &#10801;)
• U+2A34 MULTIPLICATION SIGN IN LEFT HALF CIRCLE (HTML &#10804;)
• U+2A35 MULTIPLICATION SIGN IN RIGHT HALF CIRCLE (HTML &#10805;)
• U+2A36 CIRCLED MULTIPLICATION SIGN WITH CIRCUMFLEX ACCENT (HTML &#10806;)
• U+2A37 MULTIPLICATION SIGN IN DOUBLE CIRCLE (HTML &#10807;)
• U+2A3B MULTIPLICATION SIGN IN TRIANGLE (HTML &#10811;)
• U+2AC1 SUBSET WITH MULTIPLICATION SIGN BELOW (HTML &#10945;)
• U+2AC2 SUPERSET WITH MULTIPLICATION SIGN BELOW (HTML &#10946;)