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You and You Only

  1. Sep 28, 2004 #1
    x is a real number, could you tell me how to prove that there will always be one and only one positive integer m such that m=< x <m+1 and one and only one positive integer n such that n< x =< n+1 ?
    Thank you.....
     
  2. jcsd
  3. Sep 28, 2004 #2

    jcsd

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    Looks like homework, read the rules on homework above (we'll help you, but we won't do it for you).
     
  4. Sep 28, 2004 #3
    Oh, Poet jcsd, I didn't know that.
    But how will Poet help me ?
     
  5. Sep 29, 2004 #4
    Suppose there are 2 sets X and Y, X={k belongs to Z : k<x}, Y={k belongs to Z : k<=x}, which means X and Y are not set zero and there should be a sup. Now you only need to let m=supX and n=supY then try to prove m belongs to X and n belongs to Y. Thats all.
     
  6. Sep 30, 2004 #5
    Thank you for helping Yourlooks, you are really new to this forum :wink:
     
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