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Can someone tell me what this symbol means?


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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. – Asaf Karagila Aug 3 '12 at 18:43
It's usually some generalization or specialization of the "union" sign, but it does greatly depend on context. – Thomas Andrews Aug 3 '12 at 18:44
My default interpretation is of disjoint union, thought it's also similar to the symbol often used coproducts. – Andrew Aug 3 '12 at 18:44
Search results for \bigsqcup on math.SE. – user2468 Aug 3 '12 at 18:52
I think it tells you where to put the staple. – Gerry Myerson Aug 3 '12 at 23:29

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 $A\bigsqcup =\{ (a,1) \vert a\in A_1\} \cup \{ (a,2) \vert a\in A_2\}$. 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 $A\cap B=\emptyset$? – Carry on Smiling Aug 4 '12 at 2:57
@Khromonkey : No, not always. See Devlin Mallory's response above. – KReiser Aug 4 '12 at 5:18
@Khromonkey Yes – i. m. soloveichik Aug 4 '12 at 12:31

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