1) What is the definition of a "unique set?"
2) What is an example of a set that is not unique and how would you prove that it is not unique?
3) According to Wikipedia, "two sets are equal if and only if their 'membership requirements' are logically equivalent." Is it sufficient to show that a set is not unique if it is logically equivalent to another set, or is this considered to be different than uniqueness?
4) If so, I'm curious about this proof that the empty set is unique. If both E and E' are defined by the same "inclusion criteria" (i.e. that they are the empty set,) isn't it redundant afterwards to show that they are subsets of each other and thus equivalent?