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Homework Help: Confused about semigroup X^x

  1. Feb 25, 2010 #1
    (Moderator's note: thread moved from "Linear & Abstract Algebra")

    problem # 12).

    Suppose X is a finite set with n elements. Show that the semigroup X^x has n^n elements.

    I'm confused. Isn't semigroup a set of functions? So when it says n elements, it actually means n functions? Also what is X^x defined as?
    Last edited by a moderator: Feb 26, 2010
  2. jcsd
  3. Feb 25, 2010 #2
    Well, if this semigroup is isomorphic to the set of functions from X to X, then n^n is clearly the right number. I looked at the semigroup page on Wikipedia and couldn't find that notation, though. Can't find it in your textbook?
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