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Beginning mathematical proof

  1. Mar 9, 2010 #1
    1. The problem statement, all variables and given/known data

    I originally made this thread for something else, but I have another problem that I need help with.

    Suppose a and b are nonzero real numbers. Prove that if a < 1/a < b < 1/b then a < -1.

    2. Relevant equations

    A hint was given for the problem: Assume a < 1/a < b < 1/b. Now prove that a < 0, and then use this fact to prove that a < -1.


    Thanks
     
    Last edited: Mar 9, 2010
  2. jcsd
  3. Mar 9, 2010 #2

    Mark44

    Staff: Mentor

    For b, you're missing the inequality in the triangle inequality.
     
  4. Mar 9, 2010 #3
    new problem bump
     
  5. Mar 9, 2010 #4
    It's not like threads go in the landfill and pollute kindergarten playgrounds after we're done with them. No need to recycle. Make a new thread when you have a new problem.

    For this problem, first think about what it means when [tex]a<\frac1a[/tex]. What values could [tex]a[/tex] have? You should identify two possibilities (two open intervals where [tex]a[/tex] could be). The second part of the inequality will let you narrow it down to one.
     
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