Verify that d : given by d(X,Y) := for defines a distance on
So, I haven't actually learned this yet in class... so I don't really understand what this is saying...
The first two are trivial. The third may be a bit tricky to prove if you get hung up on the absolute value signs. All you need to know is that is a metric. It would be easiest to label them: , , . You know from the triangle inequality that .
So now here's what you have to prove:
given that .
Spoiler: