Metric

A metric on a set is a function.

That function may be called the Distance Function; it is often called Distance.

One of two things happens:

• We invoke the three rules listed below and we create a metric for our space; our space is a set of points:
• We discover a space, a set of points, and we report it has a metric after we confirm that the three rules are followed:

If the distance between two points, X and Y, is zero, then X equals Y.

The distance going from X to Y is the same as the distance going from Y to X.

The shortest distance between two points is a straight line. The rule regarding this is called the Triangle Inequality and the idea is, should you leave X and go to a point not on the straight line–call that point Z–and then go from Z to Y, you will travel a greater distance than the distance of the straight line from X to Y.