|Minus sign||- , ./.|
|Mark||⋅ , ×|
|Divided sign||: , ÷ , /|
|Plus minus sign||± , ∓|
|Comparison sign||< , ≤ , = , ≥ , >|
|Difference sign , Nabla||∆ , ∇|
|Angle sign||∠ , ∡ , ∢ , ∟|
|Vertical , parallel||⊥ , ∥|
|Triangle , square||△ , □|
|Union , cut||∪ , ∩|
|Difference , complement||∖ , ∁|
|Subset , superset||⊂ , ⊆ , ⊇ , ⊃|
|Follow arrow||⇒ , ⇔ , ⇐|
|Conjunction , disjunction||∧ , ∨|
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 .
- as a binary minus sign for the operator for subtracting two numbers ( variables such as constants ), 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 "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 .
Representation in computer systems
The minus sign is defined and coded as follows:
|-||U + 2212||minus sign||Minus line||& # x2212;||& # 8722;||−||
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.
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
|-||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||
|∖||U + 2216||set minus||Difference set sign||Mathematical operators||
|➖||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|
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 ×
|_||I__||U + 005F||low line||Underscore||Basic Latin||
|||soft hyphae||Conditional hyphen||Latin-1, supplement|
|¯||I¯¯||U + 00AF||macron||Top line||Latin-1, supplement||
|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||
|Two-thirds quadrant||(not in Unicode)||
|Three quarters||(not in Unicode)||
|-||I——||U + 2014||em dash||Extra long stroke ( em dash ) (A)||General punctuation||
|-||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|
- (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.
|±||U + 00B1||plus-minus sign||Plus minus sign||Latin-1, supplement||
|∓||U + 2213||minus-or-plus sign||Minus plus sign||Mathematical operators||
|∸||U + 2238||dot minus||Minus sign with period||Mathematical operators||
|⊖||U + 2296||circled minus sign||Circled minus sign||Mathematical operators||
|⊟||U + 229F||squared minus sign||Framed minus sign||Mathematical operators||
- DIN 5008 : 2020-03, Section 10.2 Subtraction symbols
- DIN 5008: 2020-03, Appendix H.1 Table of punctuation marks and special characters
- APL2 Language Summary. (PDF) IBM , 2002, p. 15 , accessed on March 4, 2020 .
- 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 ).