# What does this notation |_| mean?

I don't know what it is even called so I cannot really type it out properly, sorry. I've seen things like $X$|_|$[0,1)$. The symbol in question looks like $\cup$ but without curvy, round bits, its like the bottom half of a square.

I don't know how else to describe it and it look bizarre.

Can anyone tell me? Thank you

• Is it $\sqcup$? Or $\amalg$? – Daniel Fischer Feb 17 '16 at 15:39
• $\sqcup$ is typically used to denote disjoint union. Meaning, you take the union of copies of the sets in questions but without common elements. It is standard to "make the sets disjoint" by interpreting $A\sqcup B$ to mean $(A\times\{0\})\cup (B\times\{1\})$. Similarly for unions of more than two sets. – Andrés E. Caicedo Feb 17 '16 at 15:41
• Also referred to as the "coproduct" in category theory. See Lang's Algebra. – user15994 Feb 17 '16 at 15:49
• By the way you can use detexify.kirelabs.org/classify.html to look up Latex symbols from a drawing of them. – Oscar Cunningham Feb 17 '16 at 16:43

## 1 Answer

$A\sqcup B$ is just $A\cup B$, but it gives the information that $A$ and $B$ are disjoint, i.e. $A\cap B=\emptyset$.

In probability theory, this notation can also be used for independence. For example, $X\sqcup Y$ means that the random variables $X$ and $Y$ are independent.

• That's the notation I'm looking for, thanks! – John Trail Feb 17 '16 at 18:51