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$\begingroup$

Can someone tell me what this symbol means?

$\bigsqcup$

  • 13
    It would be *extremely* helpful if you tell us where you saw it. This is like asking what does the symbol $\partial$ means. It may have different meanings in different contexts.2012-08-03
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    It's usually some generalization or specialization of the "union" sign, but it does greatly depend on context.2012-08-03
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    My default interpretation is of disjoint union, thought it's also similar to the symbol often used coproducts.2012-08-03
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    [Search results for `\bigsqcup` on math.SE](http://math.stackexchange.com/search?q=%5Cbigsqcup).2012-08-03
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    @Andrew: disjoint union is a coproduct. I'd say it is almost certainly some coproduct. In what category, it would depend on the context.2012-08-03
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    I simply meant that, though $\amalg$ seems to be the most common notation for general coproducts (not necessarily of sets), $\bigsqcup$ might have been used instead.2012-08-03
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    I think it tells you where to put the staple.2012-08-03
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    $\bigsqcup A$ is also used to denote (if existent) the smallest upper bound of a given subset $A \subseteq X$ of a partial ordering $(X, \le)$, but now that I think of it, this may also be viewed as a coproduct... Sorry.2014-06-17

2 Answers 2

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It is the disjoint union symbol- it is most commonly used informally to denote situations where you take the union of two disjoint sets. The actual definition though is more of a tagged union- intuitively, you index the sets to be unioned by some set $I$, and then the result is the collection of all the elements of each set, along with a "tag" that says which set it came from.

In your case, formally you have sets $A$ and $B$- let's re-label these $A_1$ and $A_2$. The disjoint union is $A_1 \bigsqcup A_2 =\{ (a,1) \vert a\in A_1\} \cup \{ (a,2) \vert a\in A_2\}$. So if they have some element $a$ in common, you end up with both $(a,1)$ and $(a,2)$ in your disjoint union. In the case that they have no common elements, the result is the same as the standard union.

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$A\bigsqcup B$ means that the sets are a "disjoint" union

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    Does this mean $A\cap B=\emptyset$?2012-08-04
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    @Khromonkey : No, not always. See Devlin Mallory's response above.2012-08-04
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    @Khromonkey Yes2012-08-04