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Finding least upper bounds

  1. Apr 28, 2004 #1
    I have to find the least upperbounds on N and P where x is an element of the reals and represented by the repeating decimal

    x=m.d1d2...dNdN+1...dN+P instead of underlining I meant for this to be an overline representing the repeating sequence of digits in the decimal
     
  2. jcsd
  3. Apr 29, 2004 #2

    mathman

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    The problem as stated has no answer. Both N and P are unbounded, unless there are other conditions which you haven't presented.
     
  4. Jul 23, 2004 #3

    mathwonk

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    I beg to differ with mathman.

    the fact that the decimal is repeating implies that the real number x is a fraction A/B where A and B are integers. then it makes sense to give a bound on N as well as on P in terms of A and B.

    I.e. N is the number of terms until the decimal starts to repeat and P is the length of a cycle after it starts repeating in cycles of the same length. It seems to me that if you just look at what happens when you divide A by B, you will see how to do this.
     
    Last edited: Jul 23, 2004
  5. Jul 23, 2004 #4

    mathman

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    For any specific rational x, you have specific values for N and P. However, there are no bounds when considering all rationals.
     
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