"METRIC" can refer to different concepts depending on the context. Here are some of the most common interpretations: 1. **Measurement System**: In the context of measurement, METRIC typically refers to the metric system, a decimal-based system of measurement that is used internationally. It includes units such as meters for length, kilograms for mass, and liters for volume.
Articles by others on the same topic
- : distances are nonnegative and finite.
- if and only if : distinct elements have positive distance.
- : exchanging the endpoints leaves the distance unchanged.
- : the triangle inequality.
A metric equips its underlying set with a metric space structure; the distance function and the space carrying it are distinct concepts. The second requirement distinguishes a metric from a pseudometric, which may identify distinct elements at zero distance. The symmetry requirement also explains why directed travel times, such as uphill versus downhill times, need not define a metric.
A tempting alternative on the real numbers is . It is nonnegative, symmetric, and zero exactly on equal endpoints, but fails the triangle inequality: . Checking only the first three requirements would miss the failure.