# Question about math symbol $\bigsqcup$

Can someone tell me what this symbol means?

$\bigsqcup$

• 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. Aug 3, 2012 at 18:43
• It's usually some generalization or specialization of the "union" sign, but it does greatly depend on context. Aug 3, 2012 at 18:44
• My default interpretation is of disjoint union, thought it's also similar to the symbol often used coproducts. Aug 3, 2012 at 18:44
• – user2468
Aug 3, 2012 at 18:52
• I think it tells you where to put the staple. Aug 3, 2012 at 23:29

## 2 Answers

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.

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

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