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Glyph for U+2140
Source: Noto Sans

U+2140 Double-Struck N-Ary Summation

U+2140 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 Math Symbol and is commonly used, that is, in no specific script.

The glyph is a Font composition of the glyph Glyph for U+2211 N-Ary Summation. It has a Neutral East Asian Width. In bidirectional context it acts as Other Neutral and is mirrored. The glyph can, under circumstances, be confused with 1 other glyphs. In text U+2140 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, summation is the addition of a sequence of any kind of numbers, called addends or summands; the result is their sum or total. Beside numbers, other types of values can be summed as well: functions, vectors, matrices, polynomials and, in general, elements of any type of mathematical objects on which an operation denoted "+" is defined.

Summations of infinite sequences are called series. They involve the concept of limit, and are not considered in this article.

The summation of an explicit sequence is denoted as a succession of additions. For example, summation of [1, 2, 4, 2] is denoted 1 + 2 + 4 + 2, and results in 9, that is, 1 + 2 + 4 + 2 = 9. Because addition is associative and commutative, there is no need of parentheses, and the result is the same irrespective of the order of the summands. Summation of a sequence of only one element results in this element itself. Summation of an empty sequence (a sequence with no elements), by convention, results in 0.

Very often, the elements of a sequence are defined, through a regular pattern, as a function of their place in the sequence. For simple patterns, summation of long sequences may be represented with most summands replaced by ellipses. For example, summation of the first 100 natural numbers may be written as 1 + 2 + 3 + 4 + ⋯ + 99 + 100. Otherwise, summation is denoted by using Σ notation, where ∑ { extstyle sum } is an enlarged capital Greek letter sigma. For example, the sum of the first n natural numbers can be denoted as ∑ i = 1 n i . { extstyle sum _{i=1}^{n}i.}

For long summations, and summations of variable length (defined with ellipses or Σ notation), it is a common problem to find closed-form expressions for the result. For example,

∑ i = 1 n i = n ( n + 1 ) 2 . {displaystyle sum _{i=1}^{n}i={frac {n(n+1)}{2}}.}

Although such formulas do not always exist, many summation formulas have been discovered—with some of the most common and elementary ones being listed in the remainder of this article.

Representations

System Representation
8512
UTF-8 E2 85 80
UTF-16 21 40
UTF-32 00 00 21 40
URL-Quoted %E2%85%80
HTML hex reference ⅀
Wrong windows-1252 Mojibake â…€

Related Characters

Confusables

Elsewhere

Complete Record

Property Value
Age 3.2 (2002)
Unicode Name DOUBLE-STRUCK N-ARY SUMMATION
Unicode 1 Name
Block Letterlike Symbols
General Category Math Symbol
Script Common
Bidirectional Category Other Neutral
Combining Class Not Reordered
Decomposition Type Font
Decomposition Mapping Glyph for U+2211 N-Ary Summation
Lowercase
Simple Lowercase Mapping Glyph for U+2140 Double-Struck N-Ary Summation
Lowercase Mapping Glyph for U+2140 Double-Struck N-Ary Summation
Uppercase
Simple Uppercase Mapping Glyph for U+2140 Double-Struck N-Ary Summation
Uppercase Mapping Glyph for U+2140 Double-Struck N-Ary Summation
Simple Titlecase Mapping Glyph for U+2140 Double-Struck N-Ary Summation
Titlecase Mapping Glyph for U+2140 Double-Struck N-Ary Summation
Case Folding Glyph for U+2140 Double-Struck N-Ary Summation
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+2140 Double-Struck N-Ary Summation
Grapheme Cluster Break Any
Grapheme Base
Grapheme Extend
Grapheme Link
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 Glyph for U+2211 N-Ary Summation
NFKC Quick Check No
NFKC_SCF Glyph for U+2211 N-Ary Summation
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
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+2140 Double-Struck N-Ary Summation
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+2140 Double-Struck N-Ary Summation
Script Extension
Vertical Orientation R