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Proof involving number theory

  1. Jan 2, 2005 #1
    Hello all

    I need help with the following proofs

    1. If x and y are arbitrary real numbers, prove that there is at least one real z satisfying x < z < y. (Do I just use the Archimedian Property?)

  2. jcsd
  3. Jan 2, 2005 #2
    Yep. :smile:
  4. Jan 2, 2005 #3

    matt grime

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    No. and it isn't true as stated.

    x and y must be distinct, and the requirement of being R is unnecessary, since it is true for Q (and C).

    what is (x+y)/2?
  5. Jan 2, 2005 #4
    Good catch. I was thinking of rational numbers between arbitrary reals.
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