Sets

A set is a well-defined collection of objects.

By well-defined we mean that you are able to answer the following question: "Is a particular element in the set?" For example, let's consider the collection of names of United States presidents. We can definitely answer the question, "Is Abraham Lincoln in this collection of names of U.S. presidents?" On the other hand, suppose you have a collection of large animals. Would a horse be in this collection? Most people would say yes to that question, but suppose you asked about a collie dog? You begin to understand the meaning of well-defined here when someone asks how large is large. Large, small, good, bad, young, old -- these are all terms that are not automatically well defined and could easily cause a collection of objects not to be classified as a set.