TITLE: What do we call a metric that doesn't satisfy triangle inequality?
QUESTION [5 upvotes]: According to wikipedia a metric is a function $d(x,y)$ that satisfies

non-negativity
identity of indiscernibles
symmetry
triangle inequality

What should we call $d(x,y)$ if the triangle inequality (and probably identity of indiscernibles) doesn't hold?
For example $d(x,y)=x^2+y^2-3xy$?

REPLY [7 votes]: It is called a semimetric according to Wikipedia.