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Metric Space

Alternate name

Basic definition

A metric space is a set with a global distance function that for every two of the set's points gives the distance between them as a nonnegative real number.

Detailed definition

A metric space is a set S with a global distance function (the metric g) that, for every two points x, y in S, gives the distance between them as a nonnegative real number g(x, y). A metric space must also satisfy
1.g(x, y) = 0 iff x = y, 2.g(x, y) = g(y, x), 3. The triangle inequality g(x, y) + g(y, z)>=g(x, z).

Educational grade level

college level

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