0
$\begingroup$

What is the name of the inequality $|x|+|y| \geq |x+y|$?

I remember seeing this inequality and thinking it was the triangle inequality, but that only holds if $x,y,z$ are the side lengths of a triangle and this holds for all real numbers? If so is there a name for this inequality?

$\endgroup$
2
  • 5
    $\begingroup$ Still called the "triangle" inequality. $\endgroup$
    – David Mitra
    Feb 7 '16 at 15:50
  • $\begingroup$ Why is it called that? $\endgroup$
    – Puzzled417
    Feb 7 '16 at 16:00
0
$\begingroup$

If $\bar{x}$, $\bar{y}$ are two vectors, $\bar{x}+\bar{y}$ is the vector representing the third side of the triangle when the tip of $\bar{x}$ touches the tail of $\bar{y}$.

(Look at the triangle law of adding vectors to get a sense of the respective directionalities).

The inequality translates as "Sum of lengths of two sides of a triangle is greater than length of the third side".

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.