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Math Help - A question about notation

  1. #1
    Forum Admin topsquark's Avatar
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    A question about notation

    Let S be a set and A a non-empty subset of S. A choice function f is defined as f: A \to S such that f(A) \in A.

    The last part is what is causing the problem. Does this mean that f(A) \in A implies that f(A) is a single element of the subset A? If so I can work with this, but what little experience I have says f(A) should be a subset (not a single element) of S so I'm a little confused.

    Thank you.
    -Dan
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    A choice function f is usually defined on a collection of subsets of some set S, not on a fixed subset A of S. Then for every A in the collection, f(A) is in A.

    In your scenario, strictly speaking, f cannot be applied to the whole A because f is defined on elements of A. You are right the the f(A) probably should be interpreted as {f(a) | a in A}, so, yes, f(A) is probably not an element of A or of S. Sometimes this application is denoted by f[A] to distinguish it from the regular application of a function to an element of the domain.
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    Some students have found this web page useful.
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    Forum Admin topsquark's Avatar
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    Thank you for the link. I've got it now.

    -Dan
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