Home U+2200 to U+22FF Mathematical Operators

# U+228DMultiset Multiplication

U+228D was added to Unicode in version 1.1 (1993). It belongs to the block U+2200 to U+22FF Mathematical Operators 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 not a composition. It has a Neutral East Asian Width. In bidirectional context it acts as Other Neutral and is not mirrored. The glyph can, under circumstances, be confused with 1 other glyphs. In text U+228D behaves as Alphabetic regarding line breaks. It has type Other for sentence and Other for word breaks. The Grapheme Cluster Break is Any.

In mathematics, a multiset (or bag, or mset) is a modification of the concept of a set that, unlike a set, allows for multiple instances for each of its elements. The number of instances given for each element is called the multiplicity of that element in the multiset. As a consequence, an infinite number of multisets exist which contain only elements a and b, but vary in the multiplicities of their elements:

• The set {a, b} contains only elements a and b, each having multiplicity 1 when {a, b} is seen as a multiset.
• In the multiset {a, a, b}, the element a has multiplicity 2, and b has multiplicity 1.
• In the multiset {a, a, a, b, b, b}, a and b both have multiplicity 3.

These objects are all different when viewed as multisets, although they are the same set, since they all consist of the same elements. As with sets, and in contrast to tuples, order does not matter in discriminating multisets, so {a, a, b} and {a, b, a} denote the same multiset. To distinguish between sets and multisets, a notation that incorporates square brackets is sometimes used: the multiset {a, a, b} can be denoted by [a, a, b].

The cardinality of a multiset is the sum of the multiplicities of all its elements. For example, in the multiset {a, a, b, b, b, c} the multiplicities of the members a, b, and c are respectively 2, 3, and 1, and therefore the cardinality of this multiset is 6.

Nicolaas Govert de Bruijn coined the word multiset in the 1970s, according to Donald Knuth.: 694  However, the concept of multisets predates the coinage of the word multiset by many centuries. Knuth himself attributes the first study of multisets to the Indian mathematician Bhāskarāchārya, who described permutations of multisets around 1150. Other names have been proposed or used for this concept, including list, bunch, bag, heap, sample, weighted set, collection, and suite.: 694

## Representations

System Representation
8845
UTF-8 E2 8A 8D
UTF-16 22 8D
UTF-32 00 00 22 8D
URL-Quoted %E2%8A%8D
HTML hex reference &#x228D;
Wrong windows-1252 Mojibake âŠ
HTML named entity &cupdot;

## Complete Record

Property Value
Age 1.1 (1993)
Unicode Name MULTISET MULTIPLICATION
Unicode 1 Name
Block Mathematical Operators
General Category Math Symbol
Script Common
Bidirectional Category Other Neutral
Combining Class Not Reordered
Decomposition Type None
Decomposition Mapping Multiset Multiplication
Lowercase
Simple Lowercase Mapping Multiset Multiplication
Lowercase Mapping Multiset Multiplication
Uppercase
Simple Uppercase Mapping Multiset Multiplication
Uppercase Mapping Multiset Multiplication
Simple Titlecase Mapping Multiset Multiplication
Titlecase Mapping Multiset Multiplication
Case Folding Multiset Multiplication
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 Multiset Multiplication
Grapheme Cluster Break Any
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 Casefold Multiset Multiplication
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 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 Multiset Multiplication
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 Multiset Multiplication
Script Extension
Vertical Orientation R