# Mathematical symbol for disjoint set union

In our lecture script, we use the notion of disjoint set union. It uses a special symbol to differentiate the disjoint from the usual set union, where we add an extra dot inside of the \cup symbol. Is there something like a \bigudot? Or any other way to add a centered dot to any symbol?

• Have a look at “How to look up a math symbol?” for ideas how you can easily find a particular symbol. Oct 10, 2010 at 16:16
• In my opinion, the best notation is \uplus. Feb 18, 2014 at 12:04

Edit I thought amssymb provides \cupdot which does what you want... but it doesn't.

\usepackage{MnSymbol} provides \cupdot and \bigcupdot but is incompatible with amssymb which is unfortunate.

Sometimes disjoint union is depicted using \sqcup which has the advantage of being in amssymb

• The MnSymbol package seems to do the job perfectly. I'm not using the amssymb package anyway, so their incompatibility is not a problem for me. Thanks for the hint! Oct 10, 2010 at 10:56

Another possibility to go around the problem that there is no such symbol in amssymb is to use the dot-accent: \dot{\bigcup} or also \dot\bigcup. This works for all symbols, and might very well be the reason that there are no dotted symbols in amssymb.

To let TeX treat such a new construct as an operator in terms of spacing though, you need to use \mathop and \mathbin, that's to say \mathop{\dot{\bigcup}} and \mathbin{\dot{\cup}}.

Disjoint union is also sometimes written using \coprod, since it is in fact the coproduct in the category of sets.

• Completely agree with this one. I've never used "cup with a dot in it" and always use either \coprod or \amalg (slightly smaller for inline maths). Oct 14, 2010 at 20:49
• This should really be a comment to the \coprod answer above, but I don't have any reputation. Though it is true that this symbol describes disjoint union, the usage is slightly different, I think. As described, this is the coproduct in the category of sets or what one might describe as the "exterior disjoint union" whereas the symbol with the dot is usually used for subsets of a given set to denote the union of two sets and state in passing that they are disjoint. In particular, \{1,2\} \dot\union \{3,4\} = \{1,2,3,4\} is a true statement whereas \{1,2\} \coprod \{3,4\} and \{1,2,3,4\}
– user13771
Apr 20, 2012 at 8:52

Another way is the following:

\makeatletter
\def\moverlay{\mathpalette\mov@rlay}
\def\mov@rlay#1#2{\leavevmode\vtop{%
\baselineskip\z@skip \lineskiplimit-\maxdimen
\ialign{\hfil$\m@th#1##$\hfil\cr#2\crcr}}}
\newcommand{\charfusion}[\mathord]{
#1{\ifx#1\mathop\vphantom{#2}\fi
\mathpalette\mov@rlay{#2\cr#3}
}
\ifx#1\mathop\expandafter\displaylimits\fi}
\makeatother

\newcommand{\cupdot}{\charfusion[\mathbin]{\cup}{\cdot}}
\newcommand{\bigcupdot}{\charfusion[\mathop]{\bigcup}{\cdot}}


The \charfusion macro is built on \moverlay (by D. Arseneau).

Examples:

$A\cupdot B$

$\bigcupdot_{i\in I} A_{i}$ • wouldn't \ooalign{\bigcup\cr\cdot} work here too? (With proper \mathpallete and \mathop usage of course.)
– yo'
Aug 27, 2012 at 21:26
• i also have this question Jan 28 at 19:49

A redacted version from symbols:

\newcommand{\cupdot}{\mathbin{\mathaccent\cdot\cup}}


This shows @egreg's solution, "my" solution, and @Vilietha's solution side by side: Not much difference between egreg's and mine, but maybe less to type ;-)

• Why doesn't this work with \bigcup or \bigcup@? Jan 10, 2013 at 23:55
• @JeffBurdges Well, it does work as long as you don't load amsmath, it just is not pretty. With amsmath, \bigcup is not just a math character anymore, so \mathaccent complains.
– mafp
Jan 11, 2013 at 10:51
• I fixed it with \nolimits even with amsmath loaded, still not pretty but no weird packages, thanks. Jan 13, 2013 at 3:21

If you use xelatex and unicode-math you can simply use the symbol ⊍ directly, or its alias \cupdot: $A ⊍ B \cupdot C$ renders with XITS Math as .

• You can use unicode-math with lualatex too. Oct 11, 2010 at 6:31
• The last time I tried it (about two months ago) some things like underbraces didn’t render correctly with lualatex. Is this fixed now? Oct 11, 2010 at 14:23

Here it is another way though dot not inside but above the cup:

$A \overset{\cdot}{\cup} B$ I would put plus instead of dot! would look nicer!

The easiest way to do the dot inside union is

\cdot \hspace{-12pt}\bigcup

• Why is this easiest? How does this scale when used in sub-/superscripts?
– Werner
Jul 7, 2017 at 16:37