# $\oplus$ symbol and disjoint union

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### piramido

Nov 21, 2007, 6:34:43 AM11/21/07
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Hello,

as far as I know the "official" symbol for union disjoint (between two
sets) is the \cup symbol with a dot placed in the middle. To use it,
you can define the new command \dotcup
\newcommand{\dotcup}{\ensuremath{\mathaccent\cdot\cup}}.

But what operation is symbolized by the \oplus symbol?

Kind regards,
Sascha

### Bob Tennent

Nov 21, 2007, 6:43:16 AM11/21/07
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On Wed, 21 Nov 2007 03:34:43 -0800 (PST), piramido wrote:

> But what operation is symbolized by the \oplus symbol?

http://en.wikipedia.org/wiki/Direct_sum

### piramido

Nov 21, 2007, 6:55:30 AM11/21/07
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Yes, that's right. Thank you. But what I really wanted to know is what
the symbol \uplus stands for.

Kind regards,
Sascha

### Hendrik Maryns

Nov 21, 2007, 6:45:01 AM11/21/07
to
piramido schreef:

This is not really a TeX question. You’d be better off in one of the
newsgroup with ‘symbol’ or ‘typography’ in their name.

Anyway, it is often used for exclusive or in the logic literature, or as
a dual operation for normal addition if the context requires it, or …

See http://www.unicode.org/charts/PDF/U2200.pdf, symbol 2295.

H.
--
Hendrik Maryns
http://tcl.sfs.uni-tuebingen.de/~hendrik/
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### piramido

Nov 21, 2007, 7:42:52 AM11/21/07
to
Thank you.

On 21 Nov., 12:45, Hendrik Maryns <gtw37b...@sneakemail.com> wrote:
> Anyway, it is often used for exclusive or in the logic literature, or as

> a dual operation for normal addition if the context requires it, or ...
.. but it is not used for the disjoint union, right?

Kind regards,
Sascha

### Hendrik Maryns

Nov 21, 2007, 7:27:23 AM11/21/07
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piramido schreef:

Whatever you want it to stand for. In mathematics, it is common
practice to introduce a symbol for some operations one needs in some
context. This can be anything. Only if an operation gets very common,
sometimes the notation solidifies, and one can talk about ‘the’ symbol
for it. But some symbols are just symbols that happen to sort of
express what one wants to use them for.

See the same link I sent you above, symbol \U228E, it is called
‘Multiset union’ there.

But why do you want to know? Just use the symbol as it suits your needs.

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### Bob Tennent

Nov 21, 2007, 7:51:09 AM11/21/07
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On Wed, 21 Nov 2007 03:55:30 -0800 (PST), piramido wrote:
> On 21 Nov., 12:43, Bob Tennent <B...@cs.queensu.ca> wrote:
>> On Wed, 21 Nov 2007 03:34:43 -0800 (PST), piramido wrote:
>> > as far as I know the "official" symbol for union disjoint
>> > (between two sets) is the \cup symbol with a dot placed in the middle.
>> > But what operation is symbolized by the \oplus symbol?
>>
>> http://en.wikipedia.org/wiki/Direct_sum
>
> Yes, that's right. Thank you. But what I really wanted to know is what
> the symbol \uplus stands for.

There is no "official" symbol for disjoint union (indeed, no "official"
symbol for anything). If you google for disjoint union, you'll see +,
|, oplus, upside-down pi, uplus, oplus, and even dotted cup, as you've
suggested, all used.

Bob T.

### Hendrik Maryns

Nov 21, 2007, 10:07:29 AM11/21/07
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piramido schreef:

You still don’t get it, do you? There is no official symbol for
anything. What would ‘official’ mean here?

Well, there is ISO, of course. You might want to have a look at ISO
31-11:1992 [1], but I do not know whether disjoint product is in there,
I didn’t buy it. Ah, there is a Wikipedia article, of course, which
doesn’t mention disjoint union: http://en.wikipedia.org/wiki/ISO_31-11

I also urge you to read the page referenced from there, so that you know
http://en.wikipedia.org/wiki/Mathematical_notation.

H.

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### Rasmus Villemoes

Nov 21, 2007, 7:40:13 AM11/21/07
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> Hello,
>
> as far as I know the "official" symbol for union disjoint (between two
> sets) is the \cup symbol with a dot placed in the middle.

(sorry for this OT posting)

Well, I think that depends on the discipline. I have seen this
"dotcup" used in analysis, but in my field of geometry/topology I have
only seen \sqcup used (if a special symbol is used at all, and not
just \cup with an explanation in words that the sets are disjoint).

Also, there is sometimes a semantic difference as to what is meant by
"disjoint union" of two sets. Sometimes one means simply the union of
two sets which happen to be disjoint, while in other circumstances one
_declares_ two sets to be disjoint (formally by some standard
set-theoretical construction) and then take their union. For instance
$R \sqcup R$ might be used to denote a topological space consisting of
two disjoint copies of the real line. I don't know if \dotcup and/or
\sqcup are more often used in one context or another.

--
Rasmus Villemoes
<http://home.imf.au.dk/burner/>