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Math Help - Proving a certain function is injective

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    Senior Member Pinkk's Avatar
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    Proving a certain function is injective

    Let A and B be nonempty sets such that |A| < |B|. Show there exists an injective function from \mathcal{P}(A) to \mathcal{P}(B).

    This was a question on my final and luckily I was able to omit it because I wasn't sure how to tackle this problem, but I'm curious to what the answer is. Thanks!
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    Quote Originally Posted by Pinkk View Post
    Let A and B be nonempty sets such that |A| < |B|. Show there exists an injective function from \mathcal{P}(A) to \mathcal{P}(B).

    This was a question on my final and luckily I was able to omit it because I wasn't sure how to tackle this problem, but I'm curious to what the answer is. Thanks!
    so there exists an injection f: A \to B. noe define g :\mathcal{P}(A) \to \mathcal{P}(B) by g(X)=f(X)=\{f(x): \ x \in X \}, for all X \in \mathcal{P}(A).
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