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Hi, I have what I hope is a very simple question related to unfamiliar notation. I am looking through a maths paper on a topic related to set theory which contains a symbol,

$\uplus$,

and I would like to know how, if at all, it differs from the typical

$\cup$

symbol in terms of its meaning.
The context leads me to believe that it does not in fact differ at all but since I don't even know the name of the symbol other than the latex id that I looked up, I can't seem to confirm that suspicion. Cheers

edit: it seems that the latex renderer also does not know about this obscure symbol '\cupplus' but '\uplus' does work.

edit2: thanks for all the replies! however, since everyone commented rather than providing an answer it seems I cannot grant the coveted 'answer' status to anyone. the disjoint union makes the most sense.

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    $\begingroup$ It is sometimes used for disjoint union, particularly by combinatorists. $\endgroup$
    – Dan Petersen
    Commented Apr 16, 2010 at 8:19
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    $\begingroup$ And also for the similar notion of multiset sum, see singularcontiguity.wordpress.com/2008/05/14/multiset-sum. $\endgroup$
    – user2734
    Commented Apr 16, 2010 at 8:25
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    $\begingroup$ I don't know much about set theory, but I can definitely say I have found that symbol somewhere, meaning "disjoint union". The disjoint union of (not necessarily disjoint sets) $A$ and $B$ is by definition the usual union between $A\times \{ 0\}$ and $B \times \{1\}$. $\endgroup$
    – Qfwfq
    Commented Apr 16, 2010 at 9:16
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    $\begingroup$ I too have seen this symbol being used to denote disjoint unions. However, I believe it is not quite the same as the coproduct, where one constructs disjoint union out of arbitrary sets. This one here only wants to make the fact apparent that both sets are disjoint as subsets of some set in the usual sense. $\endgroup$
    – M.G.
    Commented Apr 16, 2010 at 10:02
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    $\begingroup$ It's sometimes used to mean "$A \cup B$ (and $A \cap B = \varnothing$)" just like ${\oplus}$ in linear algebra means "$A + B$ (and $A \cap B = \{0\}$); both are horrible abuses of notation - mathoverflow.net/questions/18593/… $\endgroup$
    – François G. Dorais
    Commented Apr 16, 2010 at 13:33

2 Answers 2

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For the sake of giving a response to tag as an answer:

Some authors use this to denote a disjoint union of sets, i.e., "$A \cup B$ for sets $A, B$ where $A \cap B = \emptyset$."

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It may also denote that the union is a multi-set (and the both operands are possibly multi-sets). Then the multiplicity of an element in the result is the sum of its multiplicities in the operands, that explains the existence of the + in the symbol.

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