What are the examples of the well-defined sets?

Answer 1

A set is a gathering together into a whole of definite, distinct objects of our perception and of our thought - which are called elements of the set.

There are two ways of describing, or specifying the members of, a set. One way is by intensional definition, using a rule or semantic description:A is the set whose members are the first four positive integers.B is the set of colors of the French flag.

The second way is by extension - that is, listing each member of the set. An extensional definition is denoted by enclosing the list of members in curly brackets:C = {4, 2, 1, 3}D = {blue, white, red}.

Every element of a set must be unique; no two members may be identical. (A multiset is a generalized concept of a set that relaxes this criterion.) All set operations preserve this property. The order in which the elements of a set or multiset are listed is irrelevant (unlike for a sequence or tuple). Combining these two ideas into an example{6, 11} = {11, 6} = {11, 11, 6, 11}

because the extensional specification means merely that each of the elements listed is a member of the set.