: ÷ /
|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||∧ , ∨|
A colon (:), a colon with a middle bar (÷) or a slash (/) are used as dividing characters in the text . Fractions are represented by a fraction line that is similar to the forward slash in the text. In the formula set, the numerator and denominator of a fraction are displayed one above the other, with the now horizontal fraction line as the dividing line.
In most countries, including Germany, the colon (:) is preferred in school mathematics; In the English-speaking world and on pocket calculators , the Obelus symbol (÷) is usually used. In higher mathematics, the fractional spelling ( and rarely ) or the spelling as multiplication with the reciprocal value ( ) can be found almost exclusively, which provides the necessary clarity, especially with non-commutative multiplication. The slash (/) is found mainly in programming languages.
Note the different associativity of the operators , if applicable .
History of symbols
The oldest symbol appears to be the forward slash (/). It was first used by the English mathematician William Oughtred in his work Clavis Mathematicae, published in London in 1631.
The German scientist Gottfried Wilhelm Leibniz used the colon (:). Leibniz first used the division colon in 1684 in Acta Eruditorum . Before Leibniz, the Englishman Johnson published the symbol in a book in 1633, but only as a fraction symbol and not for the division in the narrower sense.
Johann Rahn introduced the symbol (÷) composed of a colon and a dash for division . Together with the symbol for multiplication (∗), this appears for the first time in his book Teutsche Algebra, published in 1659. Rahn's split sign is sometimes referred to as the English split sign because it is more common in the English-speaking world. However, its origin lies in Germany.
Representation in computer systems
|:||U + 003A||colon||Colon||& # x003A;||& # 58;||:|
|÷||U + 00F7||division sign||Divided sign||& # x00F7;||& # 247;||& divide;||\ div|
|∕||U + 2215||division slash||Split line||& # x2215;||& # 8725;||Note|
|⁄||U + 2044||fraction slash||Fraction line||& # x2044;||& # 8260;||& frasl;||Note|
|∶||U + 2236||ratio||(in relation to||& # x2236;||& # 8758;||\ ratio|
In ASCII - character set is merely contain the colon, which is why many older computer systems could only represent him. According to Unicode, U + 2236 is to be preferred instead of the simple colon for divisions, since the simple colon also has other semantics.
The distinction between division slash and fraction slash is ultimately of a semantic nature , even if the Unicode consortium intended something different according to a technical note: “ … the 'fraction slash' U + 2044… builds up to a skewed fraction, the 'division slash' U + 2215… builds up to a potentially large linear fraction,… ”( Murray Sargent III , German:“… the 'fraction line' U + 2044… causes an oblique fraction, the 'division line' U + 2215… causes a potentially large linear fraction Fraction [ Note: ie within the line], ... “) The division slash can be found in the unicode block mathematical operators , the fraction slash in the block for general punctuation .
Replacement with other characters
- Florian Cajori : A History of Mathematical Notations. Dover Publications, New York NY 1993, ISBN 0-486-67766-4 (reprint of the original two volume work by Open Court Publishing 1928/1929).
- Andreas de Vries: The long way of the numbers. A brief history of the decimal system. Books on Demand, Norderstedt 2011, ISBN 978-3-8423-5120-2 , p. 42.
- 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 ).
- Jason C: Difference Between Unicode FRACTION SLASH and DIVISION SLASH. In: Super User. Stack Exchange, June 1, 2015, accessed November 25, 2015 .
- Murray Sargent III: Unicode Nearly Plain-Text Encoding of Mathematics (PDF; 1.4 MB) March 10, 2010 (English) accessed on November 25, 2015