I know that $|x+y|\leq |x|+|y|$... But is it similar for $|x-y|$? That is, is $|x-y|\leq |x|+|y|$? I ask because of the following:
$x-y=x+(-y)$, so $|x+(-y)|\leq |x|+|-y|=|x|+|y|$
Is it possible that there is a "better" inequality? For example is $|x-y|\leq |x|-|y|$? My textbook only mentions the fact about $|x+y|$ but nothing about any other form.