"Consider the sets $ \emptyset , \lbrace \emptyset \rbrace , \lbrace \lbrace \emptyset \rbrace \rbrace , \lbrace \lbrace \lbrace \emptyset \rbrace \rbrace \rbrace , $ etc.; consider the pairs such as $ \lbrace \emptyset , \lbrace \emptyset \rbrace \rbrace , $ formed by any two of them; Consider the pairs formed any two such pairs, or else the mixed pairs formed by any singleton and any pair; and proceed so on ad infinitum.
Exercise Are all the sets obtained in this way distinct from one another?
I really didn't get what he asks. Does he ask question about the first sequence only, then about the second sequence of pairs and so on or does he ask about any possible mix of sets of empty sets?
Can anyone elucidate this exercise for me with suggested justification or hint how to show that they are distinct?