SOLUTION: Prove that ||x|-|u|-|y-v|| <= |x-y| + |u-v|

Algebra ->  Absolute-value -> SOLUTION: Prove that ||x|-|u|-|y-v|| <= |x-y| + |u-v|      Log On


   



Question 1096564: Prove that ||x|-|u|-|y-v|| <= |x-y| + |u-v|
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

||x|-|u|-|y-v|| <= |x-y| + |u-v|

Sorry, that's not always true because

Let x=2, u=4, y=3, v=5   

abs%28abs%28x%29%5E%22%22-abs%28u%29-abs%28y-v%29%29%3C=abs%28x-y%29%2Babs%28u-v%29

abs%28abs%282%29%5E%22%22-abs%284%29-abs%283-5%29%29%3C=abs%282-3%29%2Babs%284-5%29

abs%282%5E%22%22-4-abs%28-2%29%29%3C=abs%28-1%29%2Babs%28-1%29

abs%282%5E%22%22-4-2%29%3C=1%2B1

abs%28-4%29%3C=2

4%3C=2

That's false!

Maybe you copied it wrong.  If so, 
copy it correctly in the thank-you 
note form below and I'll get back 
to you by email.

Edwin