Question: Question 3. (i) Prove that if A is a nonempty set and is a cardinal number, then card(A) if and only if there exists a

Question 3. (i) Prove that if A is a nonempty set and is a cardinal number, then card(A) if and only if there exists a surjection f : A. (ii) Suppose that , are infinite cardinal numbers and that A= {Ai |i I }, where 1 card(I) and 1 card(Ai) for all i I. Prove that card(SA) . (Hint: This generalizes the result that a countable union of countable sets is countable.)

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