Unlike using a List, which can include duplicates, a Set does not. Take a look at the Java API definition of a Set:
A collection that contains no duplicate elements. More formally, sets contain no pair of elements e1 and e2 such that e1.equals(e2), and at most one null element. As implied by its name, this interface models the mathematical set abstraction.
As it says, that is the true definition of a set as in the math and science industries. You will often need a List for when you do not want duplicates and want things to be distinct.