U+228C Multiset
U+228C was added in Unicode version 1.1 in 1993. It belongs to the block
This character is a Math Symbol and is commonly used, that is, in no specific script.
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 mirrored. The word that U+228C forms with similar adjacent characters prevents a line break inside it.
The Wikipedia has the following information about this codepoint:
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, the order in which elements are listed 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 |
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Nº | 8844 |
UTF-8 | E2 8A 8C |
UTF-16 | 22 8C |
UTF-32 | 00 00 22 8C |
URL-Quoted | %E2%8A%8C |
HTML hex reference | ⊌ |
Wrong windows-1252 Mojibake | ⊌ |
Elsewhere
Complete Record
Property | Value |
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1.1 (1993) | |
MULTISET | |
— | |
Mathematical Operators | |
Math Symbol | |
Common | |
Other Neutral | |
Not Reordered | |
none | |
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✘ | |
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✘ | |
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✘ | |
✘ | |
✘ | |
✔ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
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Any | |
✔ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
0 | |
0 | |
0 | |
✘ | |
None | |
— | |
NA | |
Other | |
— | |
✘ | |
✘ | |
✔ | |
✘ | |
Yes | |
Yes | |
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Yes | |
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Yes | |
✘ | |
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✘ | |
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✘ | |
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✔ | |
✘ | |
✘ | |
✘ | |
✘ | |
Other | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
Other | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
✘ | |
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None | |
neutral | |
Not Applicable | |
— | |
No_Joining_Group | |
Non Joining | |
Alphabetic | |
none | |
not a number | |
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R |