Can the multiset $A=\{1,1,1,2,2,2,3,3,3,...,n,n,n\}$ be represented as $$A=\bigcup_{i=1}^{n}\{n,n,n\}$$
where $n$ is a positive integer.
Or am I using the union notation completely incorrectly? If so, is how would I define set $A$?
Note: To clarify my experience with this area of maths, I am going through high school education, and to my understanding, a multiset is simply a set with repeated elements. I also know that a multiset is written just like a regular set ($\{a, a, b, b\}$) but I don't know how to differentiate the two as it is said that $\{n,n,n\} = \{n\}$.
It looks ok, and would probably do the job. One common convention is to use double braces when writing multisets. There are also many accepted ways of expressing the above idea. Some examples: $$\{\{(1,3),(2,3),...,(n,3)\}\}$$ $$\{\{1\times 3,2\times 3,...,n\times 3\}\}$$ $$\{\{1:3,2:3,...,n:3\}\}$$ Among others.