Set:  A set is a well-defined collection of objects or ideas. 

What does it mean for a set to be well-defined?
            A set is well-defined if there is no ambiguity as to whether or not an object belongs to it, i.e., a set is defined so that we can always tell what is and what is not a member of the set.

Example:  C = {red, blue, yellow, green, purple} is well-defined since it is clear what is in the set.

Example:  In the opening problem on the previous page of this session, the solution set to the question “Who is the President?” is not a well-defined collection.  Does it mean only presidents of nations, or does it include presidents of companies?  Of universities?  Of clubs?  Do we include only those serving now or all who served in the past?  To be “well-defined” the collection description would have to settle all such questions.

Example: “The collection of good students at MSUM” is not a set. What does it mean to be “good?” Does the collection refer to past or present students? Also, does MSUM refer to Mankato, Moorhead, or some other school, college, or university? All these questions indicate the statement is ambiguous, i.e., it is not clear which students are members of this collection, hence, the collection is not well-defined.

Example:  “The collection of the currently enrolled students at Minnesota State University Moorhead with a grade point average above 3.0”, is a well-defined set since it is clear which students would belong to the collection.

Example:  “The collection of young people that are residents of Minnesota” is not a set. What does it mean be "young"? To someone that is 80 years old, a person that is 40 is young, but a 20 year old person may not consider 40 to be young. The word “young” is an ambiguous term. Hence, the collection is not well-defined.

Example:  “The collection of residents of Minnesota between the ages of 18 and 25 years old inclusive” is a well-defined set since it is fairly clear who would belong to this collection.