Hi, I was just thinking maybe we could help each other for the tests by listing the metrics and nonmetrics that we already know. That would be helpful as we already "recognize" them if ever we are asked to identify which is/is not a metric in a given list in a GRE (or any multiple choice) test.

Listed are what I can think of off hand:

1.

2. (is this true if 1 is replaced by any ?)

3. if and otherwise. (can replace 1 by any )

4. whenever is a known metric.

5. (can probably replace by any known metric or 3 by any real >0.

Here is an example of a nonmetric:

1.

Please feel free to add to the list. Motivation behind the metric would also be useful, so is the area of mathematics where it crops up.

Please feel free to correct if there are mistakes.