Question about math symbol $\bigsqcup$

Question

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. — Asaf Karagila, Aug 03 '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 03 '12 at 18:44
My default interpretation is of disjoint union, thought it's also similar to the symbol often used coproducts. — Andrew, Aug 03 '12 at 18:44
@Andrew: disjoint union is a coproduct. I'd say it is almost certainly some coproduct. In what category, it would depend on the context. — tomasz, Aug 03 '12 at 19:22
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. — Andrew, Aug 03 '12 at 19:39
$\bigsqcup A$ 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. — Stefan Mesken, Jun 17 '14 at 16:50

score 11 · Answer 1 · edited Jan 03 '19 at 19:09

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.

score 1 · Answer 2 · answered Aug 04 '12 at 02:39

1

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

answered Aug 04 '12 at 02:39

i. m. soloveichik

4,259

2

Does this mean $A\cap B=\emptyset$? – Asinomás Aug 04 '12 at 02:57
@Khromonkey : No, not always. See Devlin Mallory's response above. – KReiser Aug 04 '12 at 05:18
@Khromonkey Yes – i. m. soloveichik Aug 04 '12 at 12:31

Question about math symbol $\bigsqcup$

2 Answers2