The term "transitive set" refers to sets of sets: The set, A, is said to be transitive if and only if whenever and then . (Frankly, I had to look that up!)

Now, if , then either or x= A. Let and consider those two cases.

As for 2, recall Von Neumann's definition of the natural numbers: 0 is the empty set, 1 is the set whose only member is the 0, 2 is the set whose only members are 0 and 1, etc.