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Bell Numbers

  1. Oct 11, 2012 #1
    Our math Teacher asked us to find how many equivalence relations are there in a set of 4 elements, the set given is A={a,b,c,d} I found the solution to this problem there are 15 different ways to find an equivalence relation, but solving the problem, i looked in Internet that the number of equivalence relations (Partitions) of an n-element Set are the Bell numbers, somebody told me this is a definition and does not requiere a proof, but can this statement above be a theorem? If this is so I would like to see the proof.

    Thanks in advance

  2. jcsd
  3. Oct 11, 2012 #2


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