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How many choice functions?

  1. May 13, 2005 #1


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    If |X| = n > 0, there are 1C1nC12C1nC2...nC1nCn many choice functions from (power set of X minus empty set) P(X)\{{}} to X?
    Just curious. I'm jumping ahead a bit, but that makes sense to me. Is it correct? Is it much more difficult to understand when X is infinite?
  2. jcsd
  3. May 13, 2005 #2


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    Sounds right.

    Infinite sets make things more interesting! For instance, there might be 0 choice functions, if you deny the axiom of choice! Though, if there's at least one choice function on a set S, and S has an element with cardinality a, then there must be at least a choice functions.

    By a "choice function on S", I mean a function f:S --> US such that f(x) is in x. Or, equivalently, an element in the cartesian product of all the elements of S.
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