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Pretty simple ordered field question

  1. Apr 16, 2012 #1
    1. The problem statement, all variables and given/known data
    basically proving multiplying a negative number through an inequality changes the inequality


    2. Relevant equations
    if a > b, and c < 0,
    then the following inequality holds: ac < bc.


    3. The attempt at a solution
    I am pretty stumped on this one, i tried to prove that C is a negative number, but i dont know where to go at all
     
  2. jcsd
  3. Apr 16, 2012 #2

    Hurkyl

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    For the most part, it should be just unraveling definitions, and making use of the fact ad>bd for any positive d. (and picking a useful d)
     
  4. Apr 16, 2012 #3
    i'm still stuck, all i can think of is making the d=-c which i define when c+(-c)=0
     
  5. Apr 16, 2012 #4
    i'm still lost, i dont know why i am so bad at simple algebraic manipulations. can anyone offer more hints?
     
  6. Apr 16, 2012 #5

    Hurkyl

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    So make the substitution. How is < defined? Apply the definition both to this case, and to the case you're trying to solve, so that you can see what you need to prove.
     
  7. Apr 16, 2012 #6
    I actually ended up figuring it out, thanks tho!
     
  8. Apr 16, 2012 #7

    Hurkyl

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    Ah good!
     
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