U+2218 Ring Operator
U+2218 was added in Unicode version 1.1 in 1993. It belongs to the block
This character is a Math Symbol and is commonly used, that is, in no specific script. The character is also known as composite function and APL jot.
The glyph is not a composition. It has no designated width in East Asian texts. In bidirectional text it acts as Other Neutral. When changing direction it is not mirrored. The word that U+2218 forms with similar adjacent characters prevents a line break inside it. The glyph can be confused with one other glyph.
The CLDR project calls this character “ring operator” for use in screen reading software. It assigns these additional labels, e.g. for search in emoji pickers: composition, operator.
The Wikipedia has the following information about this codepoint:
In mathematics, function composition is an operation ∘ that takes two functions f and g, and produces a function h = g ∘ f such that h(x) = g(f(x)). In this operation, the function g is applied to the result of applying the function f to x. That is, the functions f : X → Y and g : Y → Z are composed to yield a function that maps x in domain X to g(f(x)) in codomain Z. Intuitively, if z is a function of y, and y is a function of x, then z is a function of x. The resulting composite function is denoted g ∘ f : X → Z, defined by (g ∘ f )(x) = g(f(x)) for all x in X.
The notation g ∘ f is read as "g of f ", "g after f ", "g circle f ", "g round f ", "g about f ", "g composed with f ", "g following f ", "f then g", or "g on f ", or "the composition of g and f ". Intuitively, composing functions is a chaining process in which the output of function f feeds the input of function g.
The composition of functions is a special case of the composition of relations, sometimes also denoted by . As a result, all properties of composition of relations are true of composition of functions, such as the property of associativity.
Composition of functions is different from multiplication of functions (if defined at all), and has some quite different properties; in particular, composition of functions is not commutative.
Representations
System | Representation |
---|---|
Nº | 8728 |
UTF-8 | E2 88 98 |
UTF-16 | 22 18 |
UTF-32 | 00 00 22 18 |
URL-Quoted | %E2%88%98 |
HTML hex reference | ∘ |
Wrong windows-1252 Mojibake | ∘ |
HTML named entity | ∘ |
HTML named entity | ∘ |
alias | composite function |
alias | APL jot |
LATEX | \circ |
digraph | Ob |
Related Characters
Confusables
Elsewhere
Complete Record
Property | Value |
---|---|
1.1 (1993) | |
RING OPERATOR | |
— | |
Mathematical Operators | |
Math Symbol | |
Common | |
Other Neutral | |
Not Reordered | |
none | |
|
|
✘ | |
|
|
|
|
✘ | |
|
|
|
|
|
|
|
|
|
|
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
|
|
Any | |
✔ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
0 | |
0 | |
0 | |
✘ | |
None | |
— | |
NA | |
Other | |
— | |
✘ | |
✘ | |
✔ | |
✘ | |
Yes | |
Yes | |
|
|
Yes | |
|
|
Yes | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✔ | |
✘ | |
✘ | |
✘ | |
✘ | |
Other | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
Other | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
|
|
None | |
neutral | |
Not Applicable | |
— | |
No_Joining_Group | |
Non Joining | |
Alphabetic | |
none | |
not a number | |
|
|
R |