- #1
MathematicalPhysicist
Gold Member
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i need help in proving this essential ineuality which i don't know how to prove (quite trivial isn't it):
||x|-|y||<=|x-y|
i know that my first trick is this:
|x|=|(x-y)+y|<=|(x-y)|+|y|
|x|-|y|<=|x-y|
and iv'e been told to do so also with |y| and i get to this:
|y|-|x|<=|y-x|
and then adding both inequalities give us with this:
|x-y|>=-|y-x|
here I'm pretty much puzzled, so can you help, or add some insight or hints.
btw, I'm in a hurry so if i have angried anyone by posting here, sorry!
||x|-|y||<=|x-y|
i know that my first trick is this:
|x|=|(x-y)+y|<=|(x-y)|+|y|
|x|-|y|<=|x-y|
and iv'e been told to do so also with |y| and i get to this:
|y|-|x|<=|y-x|
and then adding both inequalities give us with this:
|x-y|>=-|y-x|
here I'm pretty much puzzled, so can you help, or add some insight or hints.
btw, I'm in a hurry so if i have angried anyone by posting here, sorry!