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Math Help - Proof Question

  1. #1
    dpb
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    Proof Question

    Hi. I couldn't solve a proof problem, can you help me about this?
    the question is:

    thanks for any help =)
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by dpb View Post
    Hi. I couldn't solve a proof problem, can you help me about this?
    the question is:

    thanks for any help =)
    The contrapositive to " \text{If } |x| > 1 \text{,  then either }x > 1 \text{ or }x < -1 " is:
    " \text{If } -1 < x < 1 \text{, then } |x| < 1"

    Does this help?

    -Dan
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  3. #3
    dpb
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    actually i need a full proof but i don't know how to proof thats my problem
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by dpb View Post
    actually i need a full proof but i don't know how to proof thats my problem
    Do you know the interpretation of |x| on the number line? |x| is the distance of the point x from the origin. Does this help?

    -Dan
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  5. #5
    dpb
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    i know that but i dont know how to prove it in mathematical way =)
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  6. #6
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by dpb View Post
    i know that but i dont know how to prove it in mathematical way =)
    I think you are thinking this is a very hard thing to do and thus you are making it hard.

    Look at the definition of |x|:
    f(x)=|x|=\left\{\begin{array}{rr}x,\text{ if }x>0\\<br />
-x,\text{ if }x<0\\<br />
0,\text{ if }x=0\end{array}\right.
    (with thanks to Krizalid. I always forget how to code this one for some reason!)

    From this we know that if |x| < 1 that -1 < x < 1 by definition.

    -Dan
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  7. #7
    dpb
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    i get it, thanks
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  8. #8
    dpb
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    i can't understand how to proof by cases (it says i need to use proof by cases)
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  9. #9
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by dpb View Post
    i can't understand how to proof by cases (it says i need to use proof by cases)
    topsquark's definition gave you the cases. you consider when x is less than zero, greater than zero, and equal to zero. all these are taken care of in topsquark's definition. it could be broken down into two as suggested though: x greater than or equal to zero, and x less than zero
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  10. #10
    dpb
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    so what should i do in my case?
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