# How to prove that something is a set?

In Rotman's "An Introduction to Algebraic Topology", he insists that for any objects $A, B$ in a category $C$, $Hom(A, B)$ has to be a set. But in practice, how do you actually prove that something is a set? I am totally new to this categorical stuff and really confused. The only explanation provided in the book is that a set is a class small enough to have a cardinality. However, none of those words make sense to me.