Unformatted text preview: g : P ( A ) → P ( A ) given by g ( X ) = AX . We have already seen that this function is a surjection. Prove that, in fact, it is a bijection. Exercise 51. Let A be a nonempty set and let f : A → P ( A ) be any function. Show that f is not surjective. Hint: Consider S = { a ∈ A  a 6∈ f ( a ) } ∈ P ( A )....
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 Fall '09
 RyanDaileda
 Math

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