# sets with order

• May 21st 2013, 02:00 PM
chrisp
sets with order
Hi. Usually in set theory, Union[{1,b,d},{1,b,a}] = {1,b,d,a}]. In other words, only unique values are passed. In other words, the ordering information is lost. But for my physics problem, I need Union[{1,b,d},{1,b,a}] = {1,b,d,1,b,a}. Can someone please tell me how I would denote this type of union. In Mathematica, this would be Joining two lists. But is there a more concise mathematical notation.
Thanks.
• May 21st 2013, 02:03 PM
HallsofIvy
Re: sets with order
First you would not call that a "set" or a "union"- you are combining two "ordered multisets". And, no, there is no consise mathematical notation for that.
• May 21st 2013, 02:14 PM
Plato
Re: sets with order
Quote:

Originally Posted by chrisp
Hi. Usually in set theory, Union[{1,b,d},{1,b,a}] = {1,b,d,a}]. In other words, only unique values are passed. In other words, the ordering information is lost. But for my physics problem, I need Union[{1,b,d},{1,b,a}] = {1,b,d,1,b,a}. Can someone please tell me how I would denote this type of union. In Mathematica, this would be Joining two lists. But is there a more concise mathematical notation.

You should post this on a Mathematica users chat board.
Your question really has nothing to do with discrete mathematics.
• May 22nd 2013, 09:38 AM
emakarov
Re: sets with order
Quote:

Originally Posted by chrisp
But for my physics problem, I need Union[{1,b,d},{1,b,a}] = {1,b,d,1,b,a}. Can someone please tell me how I would denote this type of union. In Mathematica, this would be Joining two lists. But is there a more concise mathematical notation.

If you consider only the number of times elements occur in a set but do not care about the order, then you are working with multisets. If you care both about the number of occurrences and their order, then you are working with sequences (also called lists or tuples).

The notations for joining multisets or sequences are less standard the those for the union of sets. The operation of taking the union of multisets is sometimes denoted by $\uplus$. Joining sequences is called concatenation and may be denoted by * or just by juxtaposition. The main rule is to introduce your notation explicitly and use it consistently.