The difference between Metric and Ultrametric
When used as adjectives, metric means of or relating to the metric system of measurement, whereas ultrametric means describing a metric whose triangle inequality has the stronger form d(x, z) \le \max\{d(x, y), d(y, z)\} .
Metric is also noun with the meaning: a measure for something.
Metric is also verb with the meaning: to measure or analyse statistical data concerning the quality or effectiveness of a process.
check bellow for the other definitions of Metric and Ultrametric
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Metric as an adjective:
Of or relating to the metric system of measurement.
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Metric as an adjective (music):
Of or relating to the meter of a piece of music.
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Metric as an adjective (mathematics, physics):
Of or relating to distance.
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Metric as a noun:
A measure for something; a means of deriving a quantitative measurement or approximation for otherwise qualitative phenomena (especially used in engineering).
Examples:
"What metric should be used for performance evaluation?"
"What are the most important metrics to track for your business?"
"It's the most important single metric that quantifies the predictive performance."
"How to measure marketing? Use these key metrics for measuring marketing effectiveness."
"There is a lack of standard metrics."
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Metric as a noun (mathematics):
A measurement of the "distance" between two points in some metric space: it is a real-valued function d(x,y) between points x and y satisfying the following properties: (1) "non-negativity": d(x,y) \ge 0 , (2) "identity of indiscernibles": d(x,y) = 0 \mbox{ iff } x=y , (2) "symmetry": d(x,y) = d(y,x) , and (3) "triangle inequality": d(x,y) \le d(x,z) + d(z,y) .
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Metric as a noun (mathematics):
A metric tensor.
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Metric as a noun:
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Metric as a verb (transitive, aerospace, systems engineering):
To measure or analyse statistical data concerning the quality or effectiveness of a process.
Examples:
"We need to metric the status of software documentation."
"We need to metric the verification of requirements."
"We need to metric the system failures."
"The project manager is metricking the closure of the action items."
"Customer satisfaction was metricked by the marketing department."
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Ultrametric as an adjective (mathematics):
Describing a metric whose triangle inequality has the stronger form d(x, z) \le \max\{d(x, y), d(y, z)\} .