Should I repeat the element of a composite of a relation?

Question

Let's say I have to get the composite of a relation: R composite of R.

What if the elements in that composite repeat? Should I say it twice?

Example: R is a relation.

R= { (1,1), (1,2), (1,3), (2,3), (2,4), (3,1), (5,4) }

R^2= R composite R= {(1,1), (3,1), (1,2), (3,2), (1,3), (3,3), (1,3), (1,4), (1,1), (2,1)}

Note (1,3), (1,1) comes up twice

Answer 1

Note that $R^2$ is, at its most basic, a set. Therefore, for instance, $\{(1,1)\}$ is the same as $\{(1,1),(1,1)\}$. By convention, we usually only write elements in a set once, but it doesn't actually matter.