metric
C18165
concept
A metric is a function that defines a distance between elements of a set, satisfying non-negativity, identity of indiscernibles, symmetry, and the triangle inequality.
All labels observed (7)
| Label | Occurrences |
|---|---|
| metric canonical | 4 |
| canonical metric | 2 |
| hyperbolic metric | 2 |
| probability metric | 2 |
| L-infinity metric | 1 |
| distance metric | 1 |
| measure of distance | 1 |
Description generation (CDg)
The one-sentence description above was generated by prompting gpt-5.1 with the class name and this instruction.
Instruction
generate a one-sentence description for a given conceptual class. # Response Format Return only the sentence: "Description: [one-sentence description of the conceptional class]"
Input
Class: metric
Generated description
A metric is a function that defines a distance between elements of a set, satisfying non-negativity, identity of indiscernibles, symmetry, and the triangle inequality.
Instances (12)
| Instance | Via concept surface |
|---|---|
| Euclidean metric | — |
| Kolmogorov distance | probability metric |
|
Hamming
surface form:
Hamming distance
|
— |
| Hamming distance | — |
| Kobayashi metric | hyperbolic metric |
| Bergman metric | canonical metric |
| Fefferman metric in several complex variables | canonical metric |
| Hausdorff metric | — |
|
Chebyshev distance (L-infinity metric)
surface form:
Chebyshev distance
|
distance metric |
| Lévy–Prokhorov metric | probability metric |
| Mahalanobis distance | measure of distance |
| Poincaré metric | hyperbolic metric |