Home U+2190 to U+21FF Arrows
Glyph for U+21F8
Source: Noto Sans Math

U+21F8 RIGHTWARDS ARROW WITH VERTICAL STROKE

U+21F8 was added to Unicode in version 3.2 (2002). It belongs to the block U+2190 to U+21FF Arrows in the U+0000 to U+FFFF Basic Multilingual Plane.

This character is a Math Symbol and is commonly used, that is, in no specific script. The character is also known as z notation partial function.

The glyph is not a composition. It has a Neutral East Asian Width. In bidirectional context it acts as Other Neutral and is not mirrored. In text U+21F8 behaves as Alphabetic regarding line breaks. It has type Other for sentence and Other for word breaks. The Grapheme Cluster Break is Any.

The Wikipedia has the following information about this codepoint:

In mathematics, a partial function f from a set X to a set Y is a function from a subset S of X (possibly X itself) to Y. The subset S, that is, the domain of f viewed as a function, is called the domain of definition of f. If S equals X, that is, if f is defined on every element in X, then f is said to be total.

More technically, a partial function is a binary relation over two sets that associates every element of the first set to at most one element of the second set; it is thus a functional binary relation. It generalizes the concept of a (total) function by not requiring every element of the first set to be associated to exactly one element of the second set.

A partial function is often used when its exact domain of definition is not known or difficult to specify. This is the case in calculus, where, for example, the quotient of two functions is a partial function whose domain of definition cannot contain the zeros of the denominator. For this reason, in calculus, and more generally in mathematical analysis, a partial function is generally called simply a function. In computability theory, a general recursive function is a partial function from the integers to the integers; for many of them no algorithm can exist for deciding whether they are in fact total.

When arrow notation is used for functions, a partial function f {displaystyle f} from X {displaystyle X} to Y {displaystyle Y} is sometimes written as f : X ⇀ Y , {displaystyle f:X ightharpoonup Y,} f : X ↛ Y , {displaystyle f:X rightarrow Y,} or f : X ↪ Y . {displaystyle f:Xhookrightarrow Y.} However, there is no general convention, and the latter notation is more commonly used for inclusion maps or embeddings.

Specifically, for a partial function f : X ⇀ Y , {displaystyle f:X ightharpoonup Y,} and any x ∈ X , {displaystyle xin X,} one has either:

  • f ( x ) = y ∈ Y {displaystyle f(x)=yin Y} (it is a single element in Y), or
  • f ( x ) {displaystyle f(x)} is undefined.

For example, if f {displaystyle f} is the square root function restricted to the integers

f : Z → N , {displaystyle f:mathbb {Z} o mathbb {N} ,} defined by:
f ( n ) = m {displaystyle f(n)=m} if, and only if, m 2 = n , {displaystyle m^{2}=n,} m ∈ N , n ∈ Z , {displaystyle min mathbb {N} ,nin mathbb {Z} ,}

then f ( n ) {displaystyle f(n)} is only defined if n {displaystyle n} is a perfect square (that is, 0 , 1 , 4 , 9 , 16 , … {displaystyle 0,1,4,9,16,ldots } ). So f ( 25 ) = 5 {displaystyle f(25)=5} but f ( 26 ) {displaystyle f(26)} is undefined.

Representations

System Representation
8696
UTF-8 E2 87 B8
UTF-16 21 F8
UTF-32 00 00 21 F8
URL-Quoted %E2%87%B8
HTML-Escape ⇸
Wrong windows-1252 Mojibake ⇸
alias z notation partial function

Elsewhere

Complete Record

Property Value
Age 3.2 (2002)
Unicode Name RIGHTWARDS ARROW WITH VERTICAL STROKE
Unicode 1 Name
Block Arrows
General Category Math Symbol
Script Common
Bidirectional Category Other Neutral
Combining Class Not Reordered
Decomposition Type None
Decomposition Mapping Glyph for U+21F8 Rightwards Arrow with Vertical Stroke
Lowercase
Simple Lowercase Mapping Glyph for U+21F8 Rightwards Arrow with Vertical Stroke
Lowercase Mapping Glyph for U+21F8 Rightwards Arrow with Vertical Stroke
Uppercase
Simple Uppercase Mapping Glyph for U+21F8 Rightwards Arrow with Vertical Stroke
Uppercase Mapping Glyph for U+21F8 Rightwards Arrow with Vertical Stroke
Simple Titlecase Mapping Glyph for U+21F8 Rightwards Arrow with Vertical Stroke
Titlecase Mapping Glyph for U+21F8 Rightwards Arrow with Vertical Stroke
Case Folding Glyph for U+21F8 Rightwards Arrow with Vertical Stroke
ASCII Hex Digit
Alphabetic
Bidi Control
Bidi Mirrored
Composition Exclusion
Case Ignorable
Changes When Casefolded
Changes When Casemapped
Changes When NFKC Casefolded
Changes When Lowercased
Changes When Titlecased
Changes When Uppercased
Cased
Full Composition Exclusion
Default Ignorable Code Point
Dash
Deprecated
Diacritic
Emoji Modifier Base
Emoji Component
Emoji Modifier
Emoji Presentation
Emoji
Extender
Extended Pictographic
FC NFKC Closure Glyph for U+21F8 Rightwards Arrow with Vertical Stroke
Grapheme Cluster Break Any
Grapheme Base
Grapheme Extend
Grapheme Link
Hex Digit
Hyphen
ID Continue
ID Start
IDS Binary Operator
IDS Trinary Operator and
Ideographic
Indic Mantra Category
Indic Positional Category NA
Indic Syllabic Category Other
Jamo Short Name
Join Control
Logical Order Exception
Math
Noncharacter Code Point
NFC Quick Check Yes
NFD Quick Check Yes
NFKC Casefold Glyph for U+21F8 Rightwards Arrow with Vertical Stroke
NFKC Quick Check Yes
NFKD Quick Check Yes
Other Alphabetic
Other Default Ignorable Code Point
Other Grapheme Extend
Other ID Continue
Other ID Start
Other Lowercase
Other Math
Other Uppercase
Prepended Concatenation Mark
Pattern Syntax
Pattern White Space
Quotation Mark
Regional Indicator
Radical
Sentence Break Other
Soft Dotted
Sentence Terminal
Terminal Punctuation
Unified Ideograph
Variation Selector
Word Break Other
White Space
XID Continue
XID Start
Expands On NFC
Expands On NFD
Expands On NFKC
Expands On NFKD
Bidi Paired Bracket Glyph for U+21F8 Rightwards Arrow with Vertical Stroke
Bidi Paired Bracket Type None
East Asian Width Neutral
Hangul Syllable Type Not Applicable
ISO 10646 Comment
Joining Group No_Joining_Group
Joining Type Non Joining
Line Break Alphabetic
Numeric Type None
Numeric Value not a number
Simple Case Folding Glyph for U+21F8 Rightwards Arrow with Vertical Stroke
Script Extension
Vertical Orientation R