Does an unordered list make sense in a math paper, if the author defines it to be unordered?

Question

I'm reading a paper which the author describes lists of numbers $(\alpha,\beta, \gamma, ... )$ that he will study, but he says to let these lists be unordered and the numbers not necessarily distinct.

The "not necessarily distinct" part of it is fine, as lists allow for repeats, but unordered lists seem ... not rigorous.

Is this ok for the author to do? It's an old paper, published a couple of decades ago.

Similarly, there is some discussion about sets of numbers that allow for repeats - this again seems unusual, since I know sets to be objects that contain distinct numbers, e.g., the spectrum of a matrix is the set of distinct eigenvalues of the matrix.

Is all of this fine, so long as the author defines it to be that way?

Thanks,

Answer 1

It's perfectly OK as long as he makes clear what he means - as he seems to have.

Nowadays in combinatorics he might call it a multiset - but he might want to explain what that means ...