Comparison 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  ¬ 
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 lessthansign and the greaterthansign 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.
history
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.
use
mathematics
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 .
The less than sign (<) indicates a twodigit relation , the semantic assignment of which depends on the algebra used . It is implicitly assumed that the relation is evaluated as "true".
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 .
example
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.
One writes:
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 childfriendly 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.
Markup languages
In some markup languages such as HTML or XML , lessthan and greaterthan 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>
and </p>
(compare also paragraph characters and see generally under masking characters ).
linguistics
In linguistics , the greaterthan 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 " ancient Greek ἑλληνικός ἀλφάβητος > modern Greek ελληνικό αλφάβητο or in the opposite direction ελληνικό αλφάβητο < ἑλληνικός ἀλφάβητος.
Representation in computer systems
Keyboard input
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 : 201206, 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.
In macOS , the less than or equal to sign is entered with the key combination Alt+ <, the greater than or equal to sign with the key combination Alt+ ⇧+ >.
List of comparison characters
character  Unicode  meaning  character  Unicode  meaning  

=  ≠  U+003D 
U+2260 
equal / unequal  ≈  ≉  U+2248 
U+2249 
almost the same / not almost the same  
<  >  U+003C 
U+003E 
smaller / larger than  ≺  ≻  U+227A 
U+227B 
previous / next  
≤  ≥  U+2264 
U+2265 
less than / greater than or equal to  ≼  ≽  U+227C 
U+227D 
previous / next or same  
≮  ≯  U+226E 
U+226F 
not smaller / larger than  ⊀  ⊁  U+2280 
U+2281 
not preceding / following  
≰  ≱  U+2270 
U+2271 
neither less than / greater than nor equal  ⋠  ⋡  U+22E0 
U+22E1 
neither preceding / following nor equal  
≲  ≳  U+2272 
U+2273 
smaller / larger than or equivalent  ≾  ≿  U+227E 
U+227F 
preceding / following or equivalent  
⋜  ⋝  U+22DC 
U+22DD 
equal to or less / greater than  ⋞  ⋟  U+22DE 
U+22DF 
same or previous / next  
⋦  ⋧  U+22E6 
U+22E7 
smaller / larger than, but not equivalent  ⋨  ⋩  U+22E8 
U+22E9 
preceding / following, but not equivalent  
≴  ≵  U+2274 
U+2275 
neither smaller / larger than nor equivalent  ⊰  ⊱  U+22B0 
U+22B1 
previous / next in relation  
≦  ≧  U+2266 
U+2267 
smaller / larger than about equal to  ≨  ≩  U+2268 
U+2269 
less than / greater than, but not equal to  
≪  ≫  U+226A 
U+226B 
much smaller / larger than  ⋘  ⋙  U+22D8 
U+22D9 
much smaller / larger than  
≶  ≷  U+2276 
U+2277 
smaller / larger or larger / smaller than  ≸  ≹  U+2278 
U+2279 
neither smaller / larger nor larger / smaller than  
⋚  ⋛  U+22DA 
U+22DB 
less / greater than, equal or greater / less than  ⋖  ⋗  U+22D6 
U+22D7 
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 0x3E
).
Typographic variants
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:
character  Unicode  Latex  HTML  

≤  ≥  U+2264 
U+2265 
\leq 
\geq 
≤ 
≥

≦  ≧  U+2266 
U+2267 
\leqq 
\geqq 
≦ 
≧

⩽  ⩾  U+2A7D 
U+2A7E 
\leqslant 
\geqslant 
⩽ 
⩾

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 213701: 201812 and assignment T2 in accordance with the previous standard DIN 213701: 201206.
See also
Individual evidence
 ↑ 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 9780471690986 , 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 ).