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⊍

multiset multiplication

Multiset multiplication

142/256

⊍ is a set-theory union sign with a dot inside. Unicode names it multiset multiplication, combining collections where repeats count. In real papers and lecture notes it most often stands for the dotted union: a disjoint union, joining sets that share no elements.

Text symbol

What ⊍ means

Usually a disjoint union; officially, multiset multiplication.

The cup means union: everything in either set. Many textbooks, especially in German-speaking countries, put a dot on the cup to say the joined sets have nothing in common, so A B is a disjoint union. Typed text often uses ⊍ for that dotted cup, so in a proof or lecture note this is the likeliest reading.

Its Unicode name comes from multisets, collections where an item can appear several times, such as {a, a, b}. Its neighbour (cup with a plus) adds the counts of each item; ⊍, by its name, is the multiplying counterpart. That use is rare, so check how the author defines it.

Pure mathematical notation for formal writing; it has no place or meaning in casual chat.

Don't swap ⊍ and : dot and plus mark different operations.

Part of collections

Don't confuse it with

3

Questions people ask

2

Is ⊍ the same as disjoint union?

Often, yes. Many authors use the dotted cup for a disjoint union; others write or . The text's own definition settles it.

Why doesn't the dot show?

Your font lacks a good glyph for U228D. A math font such as Cambria Math or STIX shows it clearly.

How to type or find ⊍

Also called
cup with dot · union with dot · dotted union
Search it as
disjoint union · multiset · multiset product · ⊎
Shows up in
Anything that takes text · its shape is whatever your font draws
Windows (Word)
⎇Alt+XType 228D, then AltX to get ⊍.
Windows
⊞Win+Rrun charmap for the full table, or use the emoji picker's Ω symbols tab (Win .).
macOS
⌃Control+⌘Command+␣SpaceOpen the character viewer and search “multiset multiplication”.
Linux
⎈Ctrl+⇧Shift+UType 228d, then Enter or Space.
HTML
⊍
CSS
\228D
LaTeX
With the unicode-math package, \cupdot; otherwise \mathbin{\dot\cup} draws the dotted union.
Word (Windows)
Type 228D, then press AltX.
HTML
⊍
Codes and encoding1 code points
HTML decimal
⊍
HTML hex
⊍
CSS content
content: "\228D";
Each escape is closed by the next backslash; a trailing space is needed before a literal hex digit.
URL encoded
%E2%8A%8D
1
On screen
1
Code points
1
JS .length
3
UTF-8 bytes

A visible symbol can contain several code points. JS .length counts UTF-16 units; UTF-8 counts bytes.

Families this belongs to

1

Maths & numbers1,835 symbols