Set, sequence, bag, or what?

Question

I am dealing with finite collections of real numbers, which I will write in square brackets below.

In these collections, repetitions are significant, so, for example $[1,1,5,7]$ is not the same as $[1,5,7]$. This means that these collections are not sets.

Also, order is not significant, so $[3,5,9]$ is equal to $[5,3,9]$. This means that these collections can not be regarded as sequences, either.

So, if they are not sets, and they are not sequences, what are they?? Is there some existing mathematical construct that has the properties I described. I have seen them called "bags" in one paper, but I suspect the author just made up this name arbitrarily because (like me) he couldn't find an existing mathematical object with the desired properties.

Answer 1

Multiset is in common (English) use to describe "sets" in which elements may have multiplicity greater than $1$.

If you go to the Wikipedia page, you will find a number of other terms, including "bag," which I think is second in popularity.

Answer 2

You are dealing with ordered lists, also called arrays.

If there is a fixed number, $n$, of members in the list, this is also often called an $n$-tuple.   Such as a pair, triple, quaduple, pentuple, ...

Sequences are lists where often the members' values are some function of their index.

If order were not significant, you would be dealing with a multiset.