But have you ever thought of this fundamental question: ■What is a SET? "As my high school math teacher said,a set is just a collection of objects. Really?Don't you realize you have run into great trouble! ■Russell Paradox: Define a set S={xxx}.Is it true that S∈S? ■IfS∈S,then by definition of S,we must have Ss·Contradiction! If Ss,then by definition of S,we must have SES.Contradiction!But have you ever thought of this fundamental question: What is a SET? “As my high school math teacher said, a set is just a collection of objects. ” Really? Don’t you realize you have run into great trouble! Russell Paradox: Define a set . Is it true that ? If , then by definition of S, we must have . Contradiction! If , then by definition of S, we must have . Contradiction!