Reverse triangle inequality
= Reverse triangle inequality
{title2=$|d(x,z)-d(y,z)|\leq d(x,y)$}
In a <metric space>, applying the <triangle inequality> in both directions gives $|d(x,z)-d(y,z)|\leq d(x,y)$. In a <normed vector space>, its corresponding form is $|\|x\|-\|y\||\leq\|x-y\|$. In particular, distance to a fixed point is a <Lipschitz continuous> real function.