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Can someone tell me what this symbol means?

$\bigsqcup$

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    $\begingroup$ 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. $\endgroup$
    – Asaf Karagila ♦
    Aug 3, 2012 at 18:43
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    $\begingroup$ It's usually some generalization or specialization of the "union" sign, but it does greatly depend on context. $\endgroup$
    – Thomas Andrews
    Aug 3, 2012 at 18:44
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    $\begingroup$ My default interpretation is of disjoint union, thought it's also similar to the symbol often used coproducts. $\endgroup$
    – Andrew
    Aug 3, 2012 at 18:44
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    $\begingroup$ Search results for \bigsqcup on math.SE. $\endgroup$
    – user2468
    Aug 3, 2012 at 18:52
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    $\begingroup$ I think it tells you where to put the staple. $\endgroup$
    – Gerry Myerson
    Aug 3, 2012 at 23:29

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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    $\begingroup$ Does this mean $A\cap B=\emptyset$? $\endgroup$
    – Asinomás
    Aug 4, 2012 at 2:57
  • $\begingroup$ @Khromonkey : No, not always. See Devlin Mallory's response above. $\endgroup$
    – KReiser
    Aug 4, 2012 at 5:18
  • $\begingroup$ @Khromonkey Yes $\endgroup$
    – i. m. soloveichik
    Aug 4, 2012 at 12:31

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