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Need help on a proof

  1. Mar 12, 2010 #1
    1. The problem statement, all variables and given/known data

    Hi everyone, please help me with this problem set I am doing.

    A7r55.jpg

    (I'm not sure if the "-" after the N is supposed to be a -> typo or something)

    2. Relevant equations



    3. The attempt at a solution

    I'm not sure what k - 1 has to do with this claim, isn't it asking for an "n" where 2^n is greater than n^3? And then put that value in a proof?

    Thanks in advance.
     
  2. jcsd
  3. Mar 12, 2010 #2
    The problem appears to be written correctly. No typos.

    The k-1 is part of identifying the set of natural numbers for which the statement is true. So read through the statement in words not symbols....

    I'll get you started, "For all n, which are elements of the set of natural numbers except for n which are in the set of 0, 1, 2, up through...."

    So now you need to find k-1 to find out what that up through should end with. Just play with it to get an idea of where this point is.

    Then plug that in to the statement to do your proof by induction.

    Hope this helps!
     
  4. Mar 12, 2010 #3
    Oooh I see. So basically the question means:
    "Find a boundary number k, where unless n is any natural number below k, ie {0, 1, 2... k-1}, 2^n > n^3"?
    Well I just did some trial-and-error (am I supposed to do that?) and k should be 10.
    Can you give an outline of what the proof should look like? Do I simply write something along the lines of "case 1, if n is in the set of natural numbers below k, then the claim fails", plug in some number for n, and then "case 2, if n is equal or greater than k, then claim stands", plug in some number for n?
     
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