Suppose we would like to define a metric on New York City, let t : NYC × NYC → R+ is a function that measures the time it takes to travel between two points in New York City. Why doesn’t t satisfy the criteria of being a metric?
I know that a metric must satisfy triangle inequality, non-negativity, and symmetry. I feel like this satisfies all of these conditions. Why is it not a metric, though? Thanks for the help!