Minus sign
 ⁒



Mathematical signs  
arithmetic  
Plus sign  + 
Minus sign   , ./. 
Mark  ⋅ , × 
Divided sign  : , ÷ , / 
Plus minus sign  ± , ∓ 
Comparison sign  < , ≤ , = , ≥ , > 
Root sign  √ 
Percent sign  % 
Analysis  
Sum symbol  Σ 
Product mark  Π 
Difference sign , Nabla  ∆ , ∇ 
Prime  ′ 
Partial differential  ∂ 
Integral sign  ∫ 
Concatenation characters  ∘ 
Infinity symbol  ∞ 
geometry  
Angle sign  ∠ , ∡ , ∢ , ∟ 
Vertical , parallel  ⊥ , ∥ 
Triangle , square  △ , □ 
Diameter sign  ⌀ 
Set theory  
Union , cut  ∪ , ∩ 
Difference , complement  ∖ , ∁ 
Element character  ∈ 
Subset , superset  ⊂ , ⊆ , ⊇ , ⊃ 
Empty set  ∅ 
logic  
Follow arrow  ⇒ , ⇔ , ⇐ 
Universal quantifier  ∀ 
Existential quantifier  ∃ 
Conjunction , disjunction  ∧ , ∨ 
Negation sign  ¬ 
The minus sign () is used as a mathematical operator for subtraction or as a sign ( unary minus ) for a shortfall or generally for negative numbers or quantities . In the commercial area, the character ⁒ (or the character string ./.
) is used instead .
History and creation
In the 15th century it was still common to spell out the words “plus” and “minus”. In Italian and French scripts, often only the letter “ m ” was written out and given a horizontal line to better identify the symbol. This dash above the "m" explains the origin of today's minus sign.
The first minus sign in print appeared in the work Mercantile Arithmetic or Behende und Hüpsche Rechenung auff all Kauffmanschektiven by Johannes Widmann , published in Leipzig in 1489 . In handwriting, however, the minus sign was used before. The earliest sources are Widmann's records from 1481 and a German algebra from the same year. At the beginning of the 16th century, the minus sign spread more and more in Germany and Europe. It gradually replaced all other notations for subtraction .
use
The minus sign is used in mathematics and in programming languages in a number of roles:
 as a binary minus sign for the operator for subtracting two numbers ( variables such as constants ), for example
 as a unary minus sign for the formation of the (additive) opposite number , for example
 as a sign of a negative number constant , for example
These notation variants are not only used for sets of numbers, but also generally for groups written in an additive manner and are thus applied to vectors , matrices and other mathematical objects, for example .
Typography and appearance
The minus sign is shown as a short horizontal line at roughly half the letter height (only in special commercial contexts in which it can be read as "minus", it can be shown as a commercial minus sign ./. Or ⁒). The symbol is defined by its function and not by its exact appearance and is also described in DIN 5008 . There are two possible input characters listed for the minus sign: the minus line and the short line .
 The minus line is preferable as a typographically correct minus sign () in text works. It is visually identical to the horizontal line of the plus sign (+) and is therefore of the same length as this and also like the two parallel lines of the equal sign (=). In common fonts, this length corresponds to the width of the digits 0–9.
 The short stroke is the "hyphenminus" (also called "middle line" in technical terms) , which has been established since the typewriter times as a universal stroke to represent the minus sign, hyphen , dash and other dash characters. This line can be found on practically all keyboards (also on the numeric keypad , if one is available), often as the only horizontal line next to the lower underscore . It is usually shorter and mostly thicker and often deeper than the minus line (depending on the font). In programming languages , spreadsheets, etc. Usually only this sign can be used as a minus sign.
The APL programming language uses the "overbar" (can be represented as U + 00AF macron ) as a minus sign, for example in .
Representation in computer systems
Coding
The minus sign is defined and coded as follows:
character  Unicode position 
Unicode name 
designation  HTML hexadecimal 
HTML decimal 
HTML named 
Latex  Unicode block 

  U + 2212  minus sign  Minus line  & # x2212;  & # 8722;  − 
\minus

Mathematical operators 
The ASCII  character set has no dedicated minus sign, it contains only the hyphenminus (). Almost all modern computers use the Unicode standard, which was introduced in 1991, and can differentiate between the various characters that show dashes.
keyboard
On keyboards with the assignment E1 according to the German standard DIN 2137 : 201812, the minus line is entered with the key combination Alt Gr+ #. With the assignment T2 according to the previous standard DIN 2137: 201206, it is entered with the key sequence Alt Gr+ ä(dash accent) followed by Leertaste.
However, the language and input presets of most operating systems do not allow the direct entry of the minus line as a typographically correct minus sign via the keyboard; their standard keyboard layouts only contain the short stroke (the "hyphenminus"), modern computer systems and fonts are mostly based on Unicode , so that the minus stroke can be correctly displayed, processed and transferred without the need to replace it for technical reasons would. Even if the keyboard used does not normally have the minus dash, it can usually be inserted using a corresponding function of the operating system or the respective text editor .
Variants of the minus sign
character  Unicode position 
Unicode name 
designation  Unicode block  Latex 

  U + 002D  hyphenminus  Short dash (hyphenminus)  Basic Latin 


˗  U + 02D7  modifier letter minus sign  Modifying minus sign  Spacing Modifier Letters  
◌̠  U + 0320  combining minus sign below  COMBINING SUBMINUS SIGN  COMBINING DIACRITICS  
⁒  U + 2052  commercial minus sign  Commercial minus sign  General punctuation  
⁻  U + 207B  superscript minus sign  Superscript minus sign  Superscripts and subscripts  
₋  U + 208B  subscript minus sign  Subscript minus sign  Superscripts and subscripts  
  U + 2212  minus sign  Minus line  Mathematical operators 
\minus

∖  U + 2216  set minus  Difference set sign  Mathematical operators 
\setminus

➖  U + 2796  heavy minus sign  Bold minus line  Dingbats  
⧿  U + 29FF  miny  Miny ( combinatorial game theory )  Various math symbolsB  
  U + FE63  small hyphenminus  Small hyphen minus  Small variations in shape  
  U + FF0D  fullwidth hyphenminus  Fullwidth hyphen minus  Halfwidth and fullwidth shapes 
Similar characters
Unicode contains numerous characters whose basic shape is a horizontal line. The following table lists such characters
 which are not already listed in the above table "Variants of the minus sign",
 which do not have a combining sign such as B. the (actual, not freestanding) macron ,
 and which do not belong to a specific writing system ;
 and not the horizontal grid lines for 9pixel screen graphics (U + 23BA horizontal scan line1 ff.).
character  dto. 2 × after "I" 
Unicode position 
Unicode name 
designation  Unicode block  Latex 

_  I__  U + 005F  low line  Underscore  Basic Latin 
\_

 soft hyphae  Conditional hyphen  Latin1, supplement  
¯  I¯¯  U + 00AF  macron  Top line  Latin1, supplement 
\textasciimacron

ˉ  Iˉˉ  U + 02C9  modifier letter macron  Freestanding macron  Spacing Modifier Letters  
ˍ  Iˍˍ  U + 02CD  modifier letter low macron  Free standing macron below  Spacing Modifier Letters  
  I‐‐  U + 2010  hyphen  Hyphen / divis  General punctuation  
  I‑‑  U + 2011  nonbreaking hyphae  Protected hyphen  General punctuation  
  I‒‒  U + 2012  figure dash  digitwide line  General punctuation  
  I––  U + 2013  en dash  Long line (half square)  General punctuation 
\textendash

Twothirds quadrant  (not in Unicode) 
\texttwelveudash


Three quarters  (not in Unicode) 
\textthreequartersemdash


  I——  U + 2014  em dash  Extra long stroke ^{(} em dash ) ^{(A)}  General punctuation 
\textemdash

  I――  U + 2015  horizontal bar  Dash ^{(A) }^{(B)}  General punctuation  
‾  I‾‾  U + 203E  overline  Overline  General punctuation  
⁃  I⁃⁃  U + 2043  hyphen bullet  Shortstroke bullet  General punctuation  
⎯  I⎯⎯  U + 23AF  horizontal line extension  Extension of a transverse line ^{(C)}  Various technical signs  
⏤  I⏤⏤  U + 23E4  straightness  Straightness  Various technical signs  
─  I──  U + 2500  box drawings light horizontal  Element thin leftright ^{(C)}  Frame drawing  
━  I━━  U + 2501  box drawings heavy horizontal  Element thick leftright ^{(C)}  Frame drawing  
⸺  I⸺⸺  U + 2E3A  twoem dash  Double square  Additional punctuation  
⸻  I⸻⸻  U + 2E3B  threeem dash  Triple square  Additional punctuation  
?  I??  U + 10191  roman uncia sign  Roman Uncia symbol  Ancient symbols 
 ^{(C)} A sequence of several of these lines results in a continuous horizontal line without gaps.
Sign with minus sign as a component
Unicode contains numerous characters with a horizontal bar as a component that represents or is derived from a minus sign. These are mostly mathematical symbols.
The following table shows a selection.
character  Unicode position 
Unicode name 
designation  Unicode block  Latex 

±  U + 00B1  plusminus sign  Plus minus sign  Latin1, supplement 
\pm

∓  U + 2213  minusorplus sign  Minus plus sign  Mathematical operators 
\mp

∸  U + 2238  dot minus  Minus sign with period  Mathematical operators 
\dotminus

⊖  U + 2296  circled minus sign  Circled minus sign  Mathematical operators 
\ominus , \varominus

⊟  U + 229F  squared minus sign  Framed minus sign  Mathematical operators 
\boxminus

Individual evidence
 ↑ DIN 5008 : 202003, Section 10.2 Subtraction symbols
 ↑ ^{a } ^{b } ^{c } ^{d } ^{e} DIN 5008: 202003, Appendix H.1 Table of punctuation marks and special characters
 ↑ APL2 Language Summary. (PDF) IBM , 2002, p. 15 , accessed on March 4, 2020 .
 ↑ ^{a } ^{b } ^{c} Scott Pakin: The Comprehensive LaTeX Symbol List. (PDF, 8.7 MB) January 19, 2017, archived from the original on September 28, 2017 ; Retrieved on September 28, 2017 (English, linking the original results in a mirror of CTAN , the archive link compare file: Comprehensive LaTeX Symbol list.pdf ).