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Homework Help: Inequalites help!

  1. Oct 20, 2005 #1
    Hi, can someone help me with the following question? I don't know how to approach the proof :confused:

    If a < b and c < d then ac < bd is true, supply a proof.

    Thanks!
     
  2. jcsd
  3. Oct 20, 2005 #2

    Fermat

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    It's not true !

    let a = -2, b= -1 then a < b is true
    let c = 0, d = 1 then c < d is true
    but
    ac = -2*0 =0
    bd = -1*1 = -1
    and
    0 not < -1
    so
    ac < bd is not true

    if a,b,c,d are all positive, then the statement is true
     
  4. Oct 20, 2005 #3
    Oh so if a,b,c and d are all real numbers, does that mean the statement is true? How do I approach the proof :confused:
     
  5. Oct 20, 2005 #4

    Gokul43201

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    elle, do you know what a real number is ? I think you mean 'positive numbers.'

    In any case, if the question is exactly as you've written it, then it is incorrect...and perhaps that's what you should say (rather than second-guess and try to reinterpret the question so as to make it correct) .
     
  6. Oct 21, 2005 #5

    HallsofIvy

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    If a< b, c< d and either b and c are positive or a and d are positive then ac< bd.

    From a< b and c positive you get ac< bc. from c< d and b positive what do you get? Can you combine them?
     
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