|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||∧ , ∨|
Compare characters in the are mathematical notation usual characters to represent the proportions of two numbers or terms . The most important comparison symbols are the equal sign (=) as well as the greater than sign (>) and the less than sign (<). Comparison signs can be combined in many ways, for example with a tilde for equivalence . Crossed out variants represent the negation of the original relationship. Many of the combinations coincide with the meanings of other characters in most applications.
Typography and appearance
The less-than-sign and the greater-than-sign consist of a line bent in the middle with straight legs, whereby the kink angle is regularly acute (i.e. smaller than a right angle). The end points are perpendicular to each other so that the legs are of equal length; this is mostly retained in italics . The height and position of the signs regularly correspond to those of the plus sign . In most fonts, they are therefore significantly larger than Guillemets (pointed characters) and, on the other hand, significantly smaller than angle brackets . The latter also differ in that they have a much more open angle at the kink, mostly much larger than a right angle.
The symbols "and" were introduced by the English mathematician Thomas Harriot in 1631 in his work Artis Analyticae Praxis . The sign ≥ was first used by the French mathematician Pierre Bouguer in 1734.
In mathematics, comparison signs ( apart from the equal sign ) are used to form inequalities . In elementary mathematics, they denote the comparison of numbers, and they are also used as symbols for general order relations .
In the daily usage of natural numbers, it denotes the relation of a really smaller (not equally large!) Value to a really larger value. In prefix notation this means: <( a , b ) is evaluated as "true", so a is really smaller than b .
The more common form is the infix notation a < b , if a is really smaller than b .
The value of the natural number 3 is really smaller (has a lower order) than the value of the natural number 4. The order is given by the number line of the natural numbers.
The following also applies to real numbers :
Memorabilia and donkey bridges
To avoid confusion between the greater than sign and the less than sign, the comparison with a crocodile that always snaps for the bigger “bite” is sometimes seen as helpful - especially for schoolchildren: “The crocodile that always wants to eat most of it ”. In the magazine Kopf und Zahl (ZTR magazine for the treatment of arithmetic weaknesses) this motto is criticized:
“I am skeptical of such an 'explanation', as this donkey bridge is not based on mathematical logic, but is based solely on the desire for a child-friendly image. What if the reptile is just a little hungry? (...) Instead, I prefer an explanation that refers to the origin of the symbol: 'On the side on which the symbol is larger, there is also the larger number.' In this way you also get an elegant transition to 'is the same': this symbol is equally open on both sides. "
Alternatively, the less than sign can be stylized with a vertical line to a k (or K) and the greater than sign with a semicircle to a G.
In some markup languages such as HTML or XML , less-than and greater-than characters are used to identify the start and end of all (main) elements ( tags ) in their own language. In order to still be able to display such markups in HTML, the elements named
<and (also abbreviated in English) can be used as a substitute
>- for example, for the paragraph -start and end characters
</p>(compare also paragraph characters and see generally under masking characters ).
In linguistics , the greater-than sign is used to mean that the grammatical or phonetic form on the right can be derived from the form on the left. Conversely, the less than sign means that the shape on the left is or can be a derivation from the shape on the right. So here both signs are to be understood as arrowheads.
An example: " Greek alphabet " - or in the opposite direction .
Representation in computer systems
On standard German keyboards, the less than sign and the greater than sign are entered using the key to the right of the left shift key .
On German standard keyboards with the assignment T2 according to DIN 2137 : 2012-06, the less than or equal sign is entered with the key combination AltGr+ a, the greater than or equal sign with the key combination AltGr+ s.
List of comparison characters
||equal / unequal||≈||≉||
||almost the same / not almost the same|
||smaller / larger than||≺||≻||
||previous / next|
||less than / greater than or equal to||≼||≽||
||previous / next or same|
||not smaller / larger than||⊀||⊁||
||not preceding / following|
||neither less than / greater than nor equal||⋠||⋡||
||neither preceding / following nor equal|
||smaller / larger than or equivalent||≾||≿||
||preceding / following or equivalent|
||equal to or less / greater than||⋞||⋟||
||same or previous / next|
||smaller / larger than, but not equivalent||⋨||⋩||
||preceding / following, but not equivalent|
||neither smaller / larger than nor equivalent||⊰||⊱||
||previous / next in relation|
||smaller / larger than about equal to||≨||≩||
||less than / greater than, but not equal to|
||much smaller / larger than||⋘||⋙||
||much smaller / larger than|
||smaller / larger or larger / smaller than||≸||≹||
||neither smaller / larger nor larger / smaller than|
||less / greater than, equal or greater / less than||⋖||⋗||
||smaller / larger than with point|
The ASCII set includes the less than sign (code
0x3C), the equal sign (code
0x3D), and the greater than sign (code
Depending on the tradition of the formula set , slightly different variants are used for the less than or equal to and greater than or equal to sign:
In DIN 1302 “General mathematical symbols and terms” , the variants of the first line are specified for the less than or equal to and greater than or equal to symbols. It is also these characters that can be entered with the German standard keyboard ( assignment E1 ) in accordance with DIN 2137-01: 2018-12 and assignment T2 in accordance with the previous standard DIN 2137-01: 2012-06.
- Johann Friedrich Ludwig Häseler : Beginnings of arithmetic . Meyersche Buchhandlung, Lemgo 1802, part 1, p. 89.
- Clifford A. Pickover: A Passion for Mathematics: Numbers, Puzzles, Madness, Religion, and the Quest for Reality . John Wiley & Sons, 2005, ISBN 978-0-471-69098-6 , pp. 22 . ( wordpress.com ( Memento of the original from March 4, 2016 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this note. (PDF); October 2015)
- heads and tails. (PDF; 621 KB) In: JOURNAL of the Association for Learning Therapy and Dyscalculia e. V. in cooperation with the Mathematical Institutes for the Treatment of Mathematical Weaknesses (ZTR), 8th edition, 2007. Association for Learning and Dyscalculia Therapy, November 6th, 2007, p. 8 , accessed on September 1st, 2018 .
- Scott Pakin: The Comprehensive LaTeX Symbol List. (PDF, 8.7 MB) January 19, 2017, p. 61 , 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 ).