No Infinite Descent of Belonging-to Proof:[Adapted from Nerod and Shore]By contradiction. Consider S={SnnN.S is a set since we have enumerated all its elements,which are all sets. Since S is a set,there exists SE S such that Sns=. Since Sz+1∈S,Sx+1年Sx: The above contradicts the definition of sequence(Sn)nEN. DONE Implication:Think of all kinds of "sets"that have been disallowed!No Infinite Descent of Belonging-to  Implication: Think of all kinds of “sets” that have been disallowed!