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Cantor Expressions

  1. Oct 14, 2005 #1
    What is the cantor expansion of:

    A. 2
    B. 7
    C. 19
    D. 87
    E. 1000
    F. 1,000,000

    The algorithm to solve these small problems is the most difficult for me.
    The algorithm that I came up with states:
    Asub(n) N! + Asub(n-1) (n-1)! +....+ Asub(2)2! + Asub(1)1!, where
    Asub1 is an integer with 0 <= Asubi <= i for i = 1,2,....n,

    I have tried to find other information on google, and have failed. It seems there is not much help with cantor expressions. So any help would be grateful!
     
  2. jcsd
  3. Oct 14, 2005 #2

    EnumaElish

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    Have you seen http://www.rose-hulman.edu/mathjournal/2004/vol5-n1/paper4/v5n1-4do.doc [Broken]?

    This has an algorithm to convert a decimal number to Cantor.
     
    Last edited by a moderator: Apr 21, 2017 at 8:52 PM
  4. Oct 14, 2005 #3
    So do these answers make sense or am I doing it wrong?

    2 = 1*1! + 1
    7 = 2*2! + 1*1! + 2
    19 = 2*2! + 1*1! + 14
    87 = 3*3! + 2*2! + 1*1! + 64


    Thanks for your help!
     
  5. Oct 14, 2005 #4
    Im not sure how many digits you can put at the end, but it only makes sense I guess. Anyone help?
     
  6. Oct 15, 2005 #5
    2 = 1*1! + 1
    7 = 2*2! + 1*1! + 2
    19 = 3*3! + 1
    87 = 4*4! - 9

    Hrmm, how about these answers?
    Anyone have a clue?
     
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