Home U+2100 to U+214F Letterlike Symbols

# U+2147Double-Struck Italic Small E

U+2147 was added to Unicode in version 3.2 (2002). It belongs to the block U+2100 to U+214F Letterlike Symbols in the U+0000 to U+FFFF Basic Multilingual Plane.

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

The glyph is a Font composition of the glyph Latin Small Letter E. It has a Neutral East Asian Width. In bidirectional context it acts as Left To Right and is not mirrored. The glyph can, under circumstances, be confused with 1 other glyphs. In text U+2147 behaves as Alphabetic regarding line breaks. It has type Lower for sentence and Alphabetic Letter for word breaks. The Grapheme Cluster Break is Any.

The exponential function is a mathematical function denoted by f ( x ) = exp ⁡ ( x ) {displaystyle f(x)=exp(x)} or e x {displaystyle e^{x}} (where the argument x is written as an exponent). Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras. The exponential function originated from the notion of exponentiation (repeated multiplication), but modern definitions (there are several equivalent characterizations) allow it to be rigorously extended to all real arguments, including irrational numbers. Its ubiquitous occurrence in pure and applied mathematics led mathematician Walter Rudin to opine that the exponential function is "the most important function in mathematics".

The exponential function satisfies the exponentiation identity

which, along with the definition e = exp ⁡ ( 1 ) {displaystyle e=exp(1)} , shows that e n = e × ⋯ × e ⏟ n  factors {displaystyle e^{n}=underbrace {e imes cdots imes e} _{n{ ext{ factors}}}} for positive integers n, and relates the exponential function to the elementary notion of exponentiation. The base of the exponential function, its value at 1, e = exp ⁡ ( 1 ) {displaystyle e=exp(1)} , is a ubiquitous mathematical constant called Euler's number.

While other continuous nonzero functions f : R → R {displaystyle f:mathbb {R} o mathbb {R} } that satisfy the exponentiation identity are also known as exponential functions, the exponential function exp is the unique real-valued function of a real variable whose derivative is itself and whose value at 0 is 1; that is, exp ′ ⁡ ( x ) = exp ⁡ ( x ) {displaystyle exp '(x)=exp(x)} for all real x, and exp ⁡ ( 0 ) = 1. {displaystyle exp(0)=1.} Thus, exp is sometimes called the natural exponential function to distinguish it from these other exponential functions, which are the functions of the form f ( x ) = b x {displaystyle f(x)=b^{x}} , where the base b is a positive real number. The relation b x = e x ln ⁡ b {displaystyle b^{x}=e^{xln b}} for positive b and real or complex x establishes a strong relationship between these functions, which explains this ambiguous terminology.

The real exponential function can also be defined as a power series. This power series definition is readily extended to complex arguments to allow the complex exponential function exp : C → C {displaystyle exp :mathbb {C} o mathbb {C} } to be defined. The complex exponential function takes on all complex values except for 0 and is closely related to the complex trigonometric functions, as shown by Euler's formula.

Motivated by more abstract properties and characterizations of the exponential function, the exponential can be generalized to and defined for entirely different kinds of mathematical objects (for example, a square matrix or a Lie algebra).

In applied settings, exponential functions model a relationship in which a constant change in the independent variable gives the same proportional change (that is, percentage increase or decrease) in the dependent variable. This occurs widely in the natural and social sciences, as in a self-reproducing population, a fund accruing compound interest, or a growing body of manufacturing expertise. Thus, the exponential function also appears in a variety of contexts within physics, computer science, chemistry, engineering, mathematical biology, and economics.

The real exponential function is a bijection from R {displaystyle mathbb {R} } to ( 0 ; ∞ ) {displaystyle (0;infty )} . Its inverse function is the natural logarithm, denoted ln , {displaystyle ln ,} log , {displaystyle log ,} or log e ; {displaystyle log _{e};} because of this, some old texts refer to the exponential function as the antilogarithm.

## Representations

System Representation
8519
UTF-8 E2 85 87
UTF-16 21 47
UTF-32 00 00 21 47
URL-Quoted %E2%85%87
HTML hex reference &#x2147;
Wrong windows-1252 Mojibake â…‡
HTML named entity &ExponentialE;
HTML named entity &ee;
HTML named entity &exponentiale;

## Complete Record

Property Value
Age 3.2 (2002)
Unicode Name DOUBLE-STRUCK ITALIC SMALL E
Unicode 1 Name
Block Letterlike Symbols
General Category Lowercase Letter
Script Common
Bidirectional Category Left To Right
Combining Class Not Reordered
Decomposition Type Font
Decomposition Mapping Latin Small Letter E
Lowercase
Simple Lowercase Mapping Double-Struck Italic Small E
Lowercase Mapping Double-Struck Italic Small E
Uppercase
Simple Uppercase Mapping Double-Struck Italic Small E
Uppercase Mapping Double-Struck Italic Small E
Simple Titlecase Mapping Double-Struck Italic Small E
Titlecase Mapping Double-Struck Italic Small E
Case Folding Double-Struck Italic Small E
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 Double-Struck Italic Small E
Grapheme Cluster Break Any
Grapheme Base
Grapheme Extend
Hex Digit
Hyphen
ID Continue
ID Start
IDS Binary Operator
IDS Trinary Operator and
IDSU 0
ID_Compat_Math_Continue 0
ID_Compat_Math_Start 0
Ideographic
InCB None
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 Latin Small Letter E
NFKC Quick Check No
NFKC_SCF Latin Small Letter E
NFKD Quick Check No
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 Lower
Soft Dotted
Sentence Terminal
Terminal Punctuation
Unified Ideograph
Variation Selector
Word Break Alphabetic Letter
White Space
XID Continue
XID Start
Expands On NFC
Expands On NFD
Expands On NFKC
Expands On NFKD
Bidi Paired Bracket Double-Struck Italic Small E
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 Double-Struck Italic Small E
Script Extension
Vertical Orientation U