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Math Help - order axioms proof.

  1. #1
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    Unhappy order axioms proof.

    Hello all,
    Can someone please help me with the following proof? i have an exam on monday and cant figure out this one question i found online:

    Use order axioms to show that 0 < a < b & 0 < c < d implies that
    a/d < b/c. Thanks in advance.
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  2. #2
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    Quote Originally Posted by adriennerb View Post
    Hello all,
    Can someone please help me with the following proof? i have an exam on monday and cant figure out this one question i found online:

    Use order axioms to show that 0 < a < b & 0 < c < d implies that
    a/d < b/c. Thanks in advance.

    I hope I remember: \frac{a}{d}<\frac{b}{c} \Longleftrightarrow ac<bd \Longleftrightarrow ac-bd <0 \Longleftrightarrow ac-ad+ad-bd<0 \Longleftrightarrow a(c-d)+d(a-b)<0, and since the last inequality is exactly the opposite that we have by the given data ( c<d \Longrightarrow c-d<0\,,\,\,a<b \Longrightarrow a-b<0 and everybody's positive here, the correct inequality should be \frac {a}{d}>\frac{b}{c}

    Tonio
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