What ⊎ means
It adds the counts of matching items. A multiset is a collection where repeated items count separately: if one bag has two copies of a and another has one, ⊎ gives three. In Z, a formal language for software specifications, the Z Standard Version 1.0 uses it for bag union, adding occurrence counts.
The idea of counting repeats predates this glyph. Bhāskarāchārya's account of arrangements with repeated items, around 1150, is commonly credited as an early study of multisets. The English word “multiset” was coined in the 1970s.
Is ⊎ the same as ordinary union?
No. records membership; ⊎ adds counts. A set records whether an item appears, so repeated copies collapse into one member. If duplicates matter, {a, a} ⊎ {a} contains three copies of a.
Was ⊎ considered for code-point notation?
Yes, as a proposed visual prefix. In Unicode 1.0 (1991), ⊎ was considered as a compact visual prefix for code-point numbers, before the plain-text prefix U+ became practical.
Formal and technical: it signals that repeated items carry counts.
Don't replace it with when duplicate counts matter.
Don't confuse it with
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Related characters
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Questions people ask
1Why does ⊎ look different in some fonts?
It can: ⊎ is drawn by the active typeface, so stroke weight or plus placement may vary while it remains the same character.
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How to type or find ⊎
- Also called
- bag addition
- Search it as
- uplus · bag union · union plus · duplicate union · Z notation
- Shows up in
- Anything that takes text · its shape is whatever your font draws
⊎\228E⊎.U+228E; otherwise use its Unicode character picker.Codes and encoding1 code points
A visible symbol can contain several code points. JS .length counts UTF-16 units; UTF-8 counts bytes.