What is the well defined set?

Answer 1

A well defined set is one that you know exactly what is meant when you read it.

For example, the set of all people 6' 1" tall is well defined. Whenever you meet someone, if they're 6'1" tall, they're in the set. Otherwise, they're not. You know exactly what I mean. So that set is well defined.

The set of all cute shoes is not well defined. Jane just adores buckles, so any shoe with a buckle is cute to her. But Martha likes plain shoes. Buckles are big, ugly things that detract from the shoe. So a shoe with a buckle is not cute to Martha. So the set of all cute shoes is not well defined, because you can't just look at it and determine if it belongs in the set.

So the set of all buckled shoes would be well defined, but the set of all cute shoes is not.