Recognize whether a collection of objects is well-defined.
Recognize whether an element is in a set.
Rewrite a given set in roster form.
Recognize when two sets are equal.
We talk about sets every day — a set of books, a set of dishes, a set of rules. In mathematics, we often need to establish which objects we are using for a particular problem. Although we avoided using the term set, we have already discussed an important mathematical set — the set of integers.
We start by formally defining the term set and giving different ways of specifying sets. Furthermore we introduce notation for indicating membership in a set and saying when two sets are equal. We also present symbols for special sets such as the empty set and the set of integers.