Multiset Union Symbol
⊎ denotes multiset union, combining elements while respecting multiplicities.
U+228E
The symbol ⊎ is read as “multi-set union.” It’s used in mathematics to indicate a union operation that keeps track of how many times each element appears. You can copy it directly or use standard codepoint escapes in HTML, CSS, and JavaScript.
Multiset Union Symbol Meaning
⊎ (Unicode name: MULTISET UNION, U+228E) represents the union of multisets. Unlike ordinary set union, which treats each element as either present or not, multiset union preserves multiplicity: if an element occurs multiple times in each multiset, the result includes it with combined counts. This notation is common in contexts where repeated items matter, such as counting problems and formal definitions in abstract algebra and discrete math. As a Unicode math symbol, it is mostly used for technical writing rather than everyday typography.
Common uses
- •Mathematical definitions involving multisets where element counts must be preserved
- •Writing proofs and notation in discrete mathematics and combinatorics
- •Describing union-like operations for data collections that allow duplicates
- •Specifying formal semantics in logic or type theory using multiset constructs
- •Labeling equations on worksheets, textbooks, or slides about counting and aggregation
Examples
⊎ Multiset Union Symbol
- ⊎Let A ⊎ B be the multiset union of A and B.
- ⊎If x appears 2 times in A and 3 times in B, then x appears 5 times in A ⊎ B.
- ⊎Compute the multiset union: M ⊎ N.
- ⊎We define S = {a, a, b} ⊎ {a, c} for multiplicities.
- ⊎The resulting multiset after combining counts is U ⊎ V.
Variations
Ready to copy
Technical codes
| Unicode | U+228E | |
| HTML Entity | ⊎ | |
| HTML Code | ⊎ | |
| CSS | \228E | |
| Alt Code | Alt + 8846 | |
| Decimal | 8846 |
How to type Multiset Union Symbol (⊎)
On Windows
Hold Alt and type 8846 on the numeric keypad. In Word, type 228E then press Alt + X.
On Mac
Switch to the Unicode Hex Input keyboard, then hold Option and type 228E. Or press Control + Command + Space and search.
On Linux
Press Control + Shift + U, type 228e, then press Enter or Space.
Anywhere
Copy ⊎ with the button above and paste it wherever you need it — this works on every device and in every app, with no keyboard shortcut to remember.
FAQ
What does ⊎ mean?
⊎ means “multi-set union,” a union operation for multisets that preserves element multiplicities.
How do I type ⊎ on my device?
You can copy/paste it directly. For programming and styling, use the codepoint U+228E via HTML, CSS, or JavaScript escapes.
Is ⊎ the same as ordinary set union (∪)?
No. Ordinary set union (∪) ignores multiplicity, while ⊎ combines multisets while keeping counts.
What is the Unicode codepoint for ⊎?
It is U+228E (Unicode name: MULTISET UNION). The HTML entity is ⊎, CSS escape is \228E, and JavaScript escape is \u{228E}.