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Non sequential proof by induction

  1. Nov 1, 2005 #1
    I have established the relation that


    [​IMG]



    but how do you deliver a proof by induction for 2 variables???
     
    Last edited: Nov 1, 2005
  2. jcsd
  3. Nov 1, 2005 #2

    AKG

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    I can't say I understand the relation, but if you're trying to prove something of the form: For all n and k, R(n,k) where R(n,k) would be the sentence that you have in your picture (i.e. the expression above "n = 1,2,3,..."); then you can prove that:

    1) The sentence R(1,1) is true
    2) If the sentence R(1,k') is true then R(1,k'+1) is true
    3) Conclude that for all k, R(1,k) is true
    4) Show that if, for all k, R(n',k) is true then for all k, R(n'+1,k) is true
    5) Conclude that for all n, and for all k, R(n,k) is true.
     
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