1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook