How do you identify a well-defined set?

A well-defined set is one where its elements are clearly and unambiguously determined.

To identify a well-defined set, you need to ensure that there is no ambiguity about what is included in the set. This means that for any given element, you can definitively say whether it belongs to the set or not. For example, the set of all even numbers is well-defined because any number can be easily checked to see if it is even.

Consider the set of "all tall people." This set is not well-defined because "tall" is subjective and can vary from person to person. One person might consider someone tall if they are over 5 feet 8 inches, while another might set the bar at 6 feet. Therefore, the criteria for membership in the set are not clear and unambiguous.

In contrast, the set of "all people over 6 feet tall" is well-defined. Here, the criterion is specific and measurable, so you can easily determine whether any given person belongs to the set.

When defining a set, use precise language and clear criteria. For example, the set of "all prime numbers less than 20" is well-defined because prime numbers are clearly defined, and you can list them: {2, 3, 5, 7, 11, 13, 17, 19}. This clarity ensures that anyone can understand and identify the elements of the set without confusion.