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Putnam 1985 B3

  1. Jul 27, 2007 #1
    1. The problem statement, all variables and given/known data
    For the problem at this site http://www.kalva.demon.co.uk/putnam/psoln/psol859.html, how an array with n^2 elements contain 8*n elements (8 for each positive integer) when n is not equal to 8? Does that type of algebra not work with an infinite number of elements...?

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Jul 28, 2007 #2


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    The point is a_{ij}>i*j. You will run out of numbers at a finite point even if a_{ij} gets to be hugely large. It's not really a Cantor problem. The index set is the limit.
  4. Jul 28, 2007 #3
    My point is that if you think of the number of elements in the array as

    [tex]lim_{n\to \infty} n^2[/tex] then it at least seems odd that this number could be the same as [tex] lim_{n\to\infty}8n [/tex].

    So, you are saying that logic only holds for finite sets, right?
    That is probably just my ignorance of infinite set theory.
    Last edited: Jul 28, 2007
  5. Jul 28, 2007 #4


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    The point is that you can find an N such that the number of pairs (i,j) with i*j<N is greater than 8*N. You could compute this N, if I'm doing my numbers right it's less than 10000. That means the problem doesn't have much to do with infinite set theory.
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