I've been asked to show that a particular metric is actually an ultrametric. I'm a little lost, and I'll post what I have.

Here's the metric we're supposed to look at:

Let be any nonempty set. Define a metric by letting and be any number in the interval when .

And the problem is to show that this is an ultrametric, or that for all .

Here's my attempt at the proof:

First, since is a metric, we are given that . If , then . If and OR , then

The only remaining case is when .

or

I can't figure out the solution for this. It may be that I am taking the wrong approach. Any help is greatly appreciated.