# Name of the inequality $|x|+|y| \geq |x+y|$?

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?

• Still called the "triangle" inequality. Feb 7, 2016 at 15:50
• Why is it called that? Feb 7, 2016 at 16:00

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 $\bar{y}$.