Question: (5) Let X and Y be wellordered sets with minimal elements 3:0 and yo respectively. The successor of an element a: E X is the

(5) Let X and Y be wellordered sets with minimal elements 3:0 and yo respectively. The successor of an element a: E X is the least element not in {2: : z 5 :13} (which exists, by wellordering.) Let us call a function f : X > Y weakly successorpreserving if f(:co) = yo and for every IL' with successor 33' , the successor of f (at) is f (25' ) Find an example of a weakly successorpreserving f which is not successorpreserving. HINT: One kind of wellordered set is as follows: take two sequences {on} and {bn} and concatenate them, that is, put them in the order (11, a2, . . . b1, bg, . . . , meaning a,- S bj for all i, 5". You can do similarly with more than 2 sequences. (6) Suppose X ,Y and Z are sets with card(X)

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