Home: go to the homepage U+2190 to U+21FF Arrows

U+21F8Rightwards Arrow with Vertical Stroke

U+21F8 was added in Unicode version 3.2 in 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 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+21F8 forms with similar adjacent characters prevents a line break inside it.

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

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 univalent relation. It generalizes the concept of a (total) function by not requiring every element of the first set to be associated to an 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; no algorithm can exist for deciding whether an arbitrary such function is in fact total.

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

Specifically, for a partial function $f:X⇀Y,$ and any $x\in X,$ one has either:

• $f\left(x\right)=y\in Y$ (it is a single element in Y), or
• $f\left(x\right)$ is undefined.

For example, if $f$ is the square root function restricted to the integers

$f:Z\to N,$ defined by:
$f\left(n\right)=m$ if, and only if, ${m}^{2}=n,$ $m\in N,n\in Z,$

then $f\left(n\right)$ is only defined if $n$ is a perfect square (that is, $0,1,4,9,16,\dots$). So $f\left(25\right)=5$ but $f\left(26\right)$ 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 hex reference &#x21F8;
Wrong windows-1252 Mojibake â‡¸
alias z notation partial function

Complete Record

Property Value
Age (age) 3.2 (2002)
Unicode Name (na) RIGHTWARDS ARROW WITH VERTICAL STROKE
Unicode 1 Name (na1)
Block (blk) Arrows
General Category (gc) Math Symbol
Script (sc) Common
Bidirectional Category (bc) Other Neutral
Combining Class (ccc) Not Reordered
Decomposition Type (dt) none
Decomposition Mapping (dm) Rightwards Arrow with Vertical Stroke
Lowercase (Lower)
Simple Lowercase Mapping (slc) Rightwards Arrow with Vertical Stroke
Lowercase Mapping (lc) Rightwards Arrow with Vertical Stroke
Uppercase (Upper)
Simple Uppercase Mapping (suc) Rightwards Arrow with Vertical Stroke
Uppercase Mapping (uc) Rightwards Arrow with Vertical Stroke
Simple Titlecase Mapping (stc) Rightwards Arrow with Vertical Stroke
Titlecase Mapping (tc) Rightwards Arrow with Vertical Stroke
Case Folding (cf) Rightwards Arrow with Vertical Stroke
ASCII Hex Digit (AHex)
Alphabetic (Alpha)
Bidi Control (Bidi_C)
Bidi Mirrored (Bidi_M)
Composition Exclusion (CE)
Case Ignorable (CI)
Changes When Casefolded (CWCF)
Changes When Casemapped (CWCM)
Changes When NFKC Casefolded (CWKCF)
Changes When Lowercased (CWL)
Changes When Titlecased (CWT)
Changes When Uppercased (CWU)
Cased (Cased)
Full Composition Exclusion (Comp_Ex)
Default Ignorable Code Point (DI)
Dash (Dash)
Deprecated (Dep)
Diacritic (Dia)
Emoji Modifier Base (EBase)
Emoji Component (EComp)
Emoji Modifier (EMod)
Emoji Presentation (EPres)
Emoji (Emoji)
Extender (Ext)
Extended Pictographic (ExtPict)
FC NFKC Closure (FC_NFKC) Rightwards Arrow with Vertical Stroke
Grapheme Cluster Break (GCB) Any
Grapheme Base (Gr_Base)
Grapheme Extend (Gr_Ext)
Hex Digit (Hex)
Hyphen (Hyphen)
ID Continue (IDC)
ID Start (IDS)
IDS Binary Operator (IDSB)
IDS Trinary Operator and (IDST)
IDSU (IDSU) 0
ID_Compat_Math_Continue (ID_Compat_Math_Continue) 0
ID_Compat_Math_Start (ID_Compat_Math_Start) 0
Ideographic (Ideo)
InCB (InCB) None
Indic Mantra Category (InMC)
Indic Positional Category (InPC) NA
Indic Syllabic Category (InSC) Other
Jamo Short Name (JSN)
Join Control (Join_C)
Logical Order Exception (LOE)
Math (Math)
Noncharacter Code Point (NChar)
NFC Quick Check (NFC_QC) Yes
NFD Quick Check (NFD_QC) Yes
NFKC Casefold (NFKC_CF) Rightwards Arrow with Vertical Stroke
NFKC Quick Check (NFKC_QC) Yes
NFKC_SCF (NFKC_SCF) Rightwards Arrow with Vertical Stroke
NFKD Quick Check (NFKD_QC) Yes
Other Alphabetic (OAlpha)
Other Default Ignorable Code Point (ODI)
Other Grapheme Extend (OGr_Ext)
Other ID Continue (OIDC)
Other ID Start (OIDS)
Other Lowercase (OLower)
Other Math (OMath)
Other Uppercase (OUpper)
Prepended Concatenation Mark (PCM)
Pattern Syntax (Pat_Syn)
Pattern White Space (Pat_WS)
Quotation Mark (QMark)
Regional Indicator (RI)
Sentence Break (SB) Other
Soft Dotted (SD)
Sentence Terminal (STerm)
Terminal Punctuation (Term)
Unified Ideograph (UIdeo)
Variation Selector (VS)
Word Break (WB) Other
White Space (WSpace)
XID Continue (XIDC)
XID Start (XIDS)
Expands On NFC (XO_NFC)
Expands On NFD (XO_NFD)
Expands On NFKC (XO_NFKC)
Expands On NFKD (XO_NFKD)
Bidi Paired Bracket (bpb) Rightwards Arrow with Vertical Stroke
Bidi Paired Bracket Type (bpt) None
East Asian Width (ea) neutral
Hangul Syllable Type (hst) Not Applicable
ISO 10646 Comment (isc)
Joining Group (jg) No_Joining_Group
Joining Type (jt) Non Joining
Line Break (lb) Alphabetic
Numeric Type (nt) none
Numeric Value (nv) not a number
Simple Case Folding (scf) Rightwards Arrow with Vertical Stroke
Script Extension (scx)
Vertical Orientation (vo) R