Home U+2000 to U+206F General Punctuation

# U+2061Function Application

U+2061 was added to Unicode in version 3.2 (2002). It belongs to the block U+2000 to U+206F General Punctuation in the U+0000 to U+FFFF Basic Multilingual Plane.

This character is a Format and is commonly used, that is, in no specific script.

The glyph is not a composition. It has a Neutral East Asian Width. In bidirectional context it acts as Boundary Neutral and is not mirrored. In text U+2061 behaves as Alphabetic regarding line breaks. It has type Format for sentence and Format for word breaks. The Grapheme Cluster Break is Control.

In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

The earliest known approach to the notion of function can be traced back to works of Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a function of time. Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable (that is, they had a high degree of regularity). The concept of a function was formalized at the end of the 19th century in terms of set theory, and this greatly enlarged the domains of application of the concept.

A function is most often denoted by letters such as f, g and h, and the value of a function f at an element x of its domain is denoted by f(x); the numerical value resulting from the function evaluation at a particular input value is denoted by replacing x with this value; for example, the value of f at x = 4 is denoted by f(4). When the function is not named and is represented by an expression E, the value of the function at, say, x = 4 may be denoted by E|x=4. For example, the value at 4 of the function that maps x to ( x + 1 ) 2 {displaystyle (x+1)^{2}} may be denoted by ( x + 1 ) 2 | x = 4 {displaystyle left.(x+1)^{2} ightvert _{x=4}} (which results in 25).

A function is uniquely represented by the set of all pairs (x, f (x)), called the graph of the function, a popular means of illustrating the function. When the domain and the codomain are sets of real numbers, each such pair may be thought of as the Cartesian coordinates of a point in the plane.

Functions are widely used in science, engineering, and in most fields of mathematics. It has been said that functions are "the central objects of investigation" in most fields of mathematics.

## Representations

System Representation
8289
UTF-8 E2 81 A1
UTF-16 20 61
UTF-32 00 00 20 61
URL-Quoted %E2%81%A1
HTML hex reference &#x2061;
Wrong windows-1252 Mojibake â¡
HTML named entity &ApplyFunction;
HTML named entity &af;

## Complete Record

Property Value
Age 3.2 (2002)
Unicode Name FUNCTION APPLICATION
Unicode 1 Name
Block General Punctuation
General Category Format
Script Common
Bidirectional Category Boundary Neutral
Combining Class Not Reordered
Decomposition Type None
Decomposition Mapping Function Application
Lowercase
Simple Lowercase Mapping Function Application
Lowercase Mapping Function Application
Uppercase
Simple Uppercase Mapping Function Application
Uppercase Mapping Function Application
Simple Titlecase Mapping Function Application
Titlecase Mapping Function Application
Case Folding Function Application
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 Function Application
Grapheme Cluster Break Control
Grapheme Base
Grapheme Extend
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 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
Sentence Break Format
Soft Dotted
Sentence Terminal
Terminal Punctuation
Unified Ideograph
Variation Selector
Word Break Format
White Space
XID Continue
XID Start
Expands On NFC
Expands On NFD
Expands On NFKC
Expands On NFKD
Bidi Paired Bracket Function Application
Bidi Paired Bracket Type None
East Asian Width Neutral
Hangul Syllable Type Not Applicable
ISO 10646 Comment
Joining Group No_Joining_Group
Joining Type Transparent
Line Break Alphabetic
Numeric Type None
Numeric Value not a number
Simple Case Folding Function Application
Script Extension
Vertical Orientation R