Notation for set union that results in a multiset

Question

Is there a notation that replaces the "union" operator $A\cup B$ and emphasizes that the outcome should be considered a multi-set rather than a set? For example, if $A = \{1,2,3\}$ and $B =\{3,4,5\}$, then:

$$A ? B = \{1,2,3,3,4,5\}$$

since the $3$ is counted twice. What operator can I used instead of the "$?$"?

Answer 1

This is sometimes called “additive union”. (For example, see Blizard, W. “Multiset Theory”.) There is no truly standard notation for multiset operations, but $$A\uplus B$$ is often used for additive union. The MathJax code is \uplus.

Answer 2

For multiset union (and intersection, etc) just use the usual symbols. Just make clear you are talking multisets, not sets.