In trying to solve the following inequality in R:
|x+y| |y+z|+|z+x| |x+y+z| |x| +|y| + |z|,i tried a proof by contradiction.
So suppose the above inequality is not true ,then we have:
|x+y| |y+z|+|z+x| > |x+y+z| |x| +|y| + |z|
....................or 2|x| +2|y| +2|z| > |x+y+z| +|x| +|y| +|z|
.....................or |x| +|y| + |z|> |x+y+z| and here is where i get stuck because i cannot derive a contradiction
It is one of those things that no body can explain. I must have gone at least 10 times over my opening post ,yet a terrible mistake has escape my attention .
I am terribly sorry the correct inequality is:
|x+y|+|y+z|+|z+x| |x|+|y|+|z|+|x+y+z|