Concatenation characters
∘



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 concatenation symbol ( ), also known as a circle operator , is a mathematical symbol that expresses the concatenation of two functions , relations or words . If there is no risk of confusion with multiplication , it is often left out.
use
Chaining of functions
The pipe symbol is often used as mathematical operator for the sequential execution of functions used. If sets are and as well as functions, then the concatenation of and through
written down. The expression “ ” is read as “ linked with ”, “ composed with ”, “ after ” or “ kringel ”. When using the notation, it is important to ensure that the composition is carried out from right to left, i.e. that it is applied first and then . Occasionally, however, the reverse order is used and written in the literature .
Chaining of relations
More generally, the concatenation character is used as an operator for concatenating binary relations . If sets and as well as binary relations are again , then the concatenation of and through
written down. The result is called a relation product or a relative product. Here, too, the reverse order is occasionally used.
Concatenation of words
In theoretical computer science , the concatenation character is used for the concatenation of words . If and are two words above an alphabet , then the concatenation of and through
written down. Here is the prefix and the suffix of the result of the concatenation. The concatenation of words is a special case of a concatenation of sets .
Binary links
In an even more general way, the concatenation symbol is sometimes used alongside the characters , and as a placeholder for binary combinations of general algebraic structures .
Presentation on the computer
Coding
The concatenation character is defined and coded as follows:
character  Unicode  designation  HTML  Latex  

position  designation  hexadecimal  decimal  named  
∘ 
U+2218

ring operator  Circle operator 
∘

∘

\circ

Similar characters
character  Unicode  Surname  

position  designation  
O 
U+006F

Latin small letter or similar  Latin Small Letter O 
° 
U+00B0

degree sign  Degree sign 
ο 
U+03BF

greek small letter omicron  Greek Small Letter Omicron 
о 
U+043E

cyrillic small letter о  Cyrillic lowercase letter о 
ₒ 
U+2092

Latin subscript small letter or similar  Subscript Latin small letter o 
○ 
U+25CB

white circle  White circle 
◦ 
U+25E6

white bullet  White bullet 
⚬ 
U+26AC

medium small white circle  Middle small white circle 
。 
U+3002

ideographic full stop  End of sentence in CJK fonts 
Individual evidence
 ↑ Gerd Fischer: Linear Algebra . Springer, 2009, p. 36 .
 ↑ Ehrhard Behrends: Analysis Volume 1 . Springer, 2014, p. 19 .
 ↑ George Hoever: Higher Mathematics compact . Springer, 2013, p. 43 .