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.
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.
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 . 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.