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

${\displaystyle 36-5=31}$

• as a unary minus sign for the formation of the (additive) opposite number , for example

${\displaystyle -({-x})=x}$

• as a sign of a negative number constant , for example

${\displaystyle -6{,}25}$

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 "hyphen-minus" (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 . ${\displaystyle {}^{-}6.25}$

Representation in computer systems

Coding

The minus sign is defined and coded as follows:

International character encoding standard  Unicode
and encoding in the Internet document format HTML as well as in LaTeX

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 hyphen-minus (-). 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 : 2018-12, the minus line is entered with the key combination Alt Gr+ #. With the assignment T2 according to the previous standard DIN 2137: 2012-06, 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 "hyphen-minus"), 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	hyphen-minus	Short dash (hyphen-minus)	Basic Latin	-
˗	U + 02D7	modifier letter minus sign	Modifying minus sign	Spacing Modifier Letters
◌̠	U + 0320	combining minus sign below	COMBINING SUB-MINUS 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 symbols-B
-	U + FE63	small hyphen-minus	Small hyphen minus	Small variations in shape
-	U + FF0D	fullwidth hyphen-minus	Full-width hyphen minus	Half-width and full-width 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 free-standing) macron ,
• and which do not belong to a specific writing system ;
• and not the horizontal grid lines for 9-pixel screen graphics (U + 23BA horizontal scan line-1 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	Latin-1, supplement
¯	I¯¯	U + 00AF	macron	Top line	Latin-1, 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	non-breaking hyphae	Protected hyphen	General punctuation
-	I‒‒	U + 2012	figure dash	digit-wide line	General punctuation
-	I––	U + 2013	en dash	Long line (half square)	General punctuation	\textendash
				Two-thirds 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	Short-stroke 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 left-right (C)	Frame drawing
━	I━━	U + 2501	box drawings heavy horizontal	Element thick left-right (C)	Frame drawing
⸺	I⸺⸺	U + 2E3A	two-em dash	Double square	Additional punctuation
⸻	I⸻⸻	U + 2E3B	three-em dash	Triple square	Additional punctuation
?	I??	U + 10191	roman uncia sign	Roman Uncia symbol	Ancient symbols

^(A)A sequence of several of these lines can contain gaps due to the page spacing declared in the glyph .

^(B)As a rule, this character resembles an em dash in length, shape and height and differs from this only in its line break properties.

^(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	plus-minus sign	Plus minus sign	Latin-1, supplement	\pm
∓	U + 2213	minus-or-plus 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

1. ↑ DIN 5008 : 2020-03, Section 10.2 Subtraction symbols
2. ↑ ^{a b c d e} DIN 5008: 2020-03, Appendix H.1 Table of punctuation marks and special characters
3. ↑ APL2 Language Summary. (PDF) IBM , 2002, p. 15 , accessed on March 4, 2020 . 
4. ↑ ^{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 ).