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March 12th, 2009, 11:09 PM
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| |  Absolute Value + Inequality Proofs
Got a couple proofs I'm stuck on.....
1. Prove |x| > a iff x > a or x < -a
I know it has a couple different cases...but from there...I'm lost! yikes!
2. Prove |x| - |y| < |x-y|
Again, I know it has to do with the triangle inequality...but everything I try doesn't seem to get me anywhere.... |
March 13th, 2009, 08:50 AM
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Quote:
Originally Posted by mikijo  Got a couple proofs I'm stuck on.....
1. Prove |x| > a iff x > a or x < -a
I know it has a couple different cases...but from there...I'm lost! yikes!
2. Prove |x| - |y| < |x-y|
Again, I know it has to do with the triangle inequality...but everything I try doesn't seem to get me anywhere.... | Triangle inequality  so  then let  . |
March 13th, 2009, 10:09 AM
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Quote:
Originally Posted by mikijo Got a couple proofs I'm stuck on.....
1. Prove |x| > a iff x > a or x < -a
I know it has a couple different cases...but from there...I'm lost! yikes!
2. Prove |x| - |y| < |x-y|
Again, I know it has to do with the triangle inequality...but everything I try doesn't seem to get me anywhere.... | and for # 1,   or  |
March 13th, 2009, 10:28 AM
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That's wrong.
When you say  or  there's an obvious contradiction.
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March 13th, 2009, 10:33 AM
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Quote:
Originally Posted by Krizalid That's wrong.
When you say or there's an obvious contradiction. | Here:
Prove |x| > a iff x > a or x < -a  or  or . Thus proving both directions.
Last edited by GaloisTheory1; March 13th, 2009 at 10:45 AM.
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