yup, that's a standard example / counterexample. Called the discrete metric. If you are trying to prove something about metric spaces, you should try your sta

yup, that's a standard example / counterexample. Called the discrete metric. If you are trying to prove something about metric spaces, you should try your statement on that metric. A lot of things that seem true because they intuitively sound right with Euclidean distance break with the discrete metric.