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February 23rd, 2017, 04:39 PM   #1
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Inequality help

Assume $\displaystyle a,b,c,d$ are positive and $\displaystyle a>b$ as well as
$\displaystyle c<d $

Can we add the the two the following way?

$\displaystyle a>b$ --- (1)
$\displaystyle d>c$ --- (2)

so $\displaystyle a+d>b+c$.

My teacher said it is wrong, but i am not able to find a counterexample.

Appreciate any help.
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February 23rd, 2017, 04:48 PM   #2
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I hate to say a teacher is wrong, but in this case ... I agree with you.

You sure about the starting inequalities? Is there a "problem" to do that you haven't stated completely?
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February 23rd, 2017, 04:54 PM   #3
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Thank you for your answer skeeter. Yes, the starting inequalities are correct, it is just a question I had in general, not a specific problem.
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February 26th, 2017, 02:43 AM   #4
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So, we travel in ℝ₊

a > b ⇒ a = b + k

d > c ⇒ d = c + m

a + d = b+k+c+m ⇒ a + d = (b+c) +(k + m) ⇒ a + d > b + c
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March 23rd, 2017, 10:05 AM   #5
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Maybe your teacher say that: it is not equivalent!

a>b AND d>c so a+d>b+c,
but the counter case is not true!
For example: 2+7>3+4, with a=2; b=3; d=7 and c=4.
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