2What is a set?

A set is a collection of objects. They could be any objects. Numbers, bowls, letters, football teams—you name it. A set is a collection in the sense that there is nothing to a set beyond the items—we call them the “elements”—it contains. That means that you can’t have two sets with the very same elements: a set is just the collection of elements, so if you’ve got the same collection, it’s the same set, not two sets.

Saying that there are two distinct sets which contain exactly the same objects is like saying that there are two distinct families which contain exactly the same people. To mean that literally is to misunderstand what a family is and what makes different families different: families are different because they have different members, just like sets are different when they have different members.