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Fix typo and wrap lines at 92 chars
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IsakFalk committed Apr 13, 2020
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Expand Up @@ -133,13 +133,13 @@ At the top of this hierarchy is an abstract class **PreMetric**, which is define

d(x, z) <= d(x, y) + d(y, z) for all x, y, z

This type system has practical significance. For example, when computing pairwise distances between a set of vectors, you may only
perform computation for half of the pairs, and derive the values immediately for the remaining halve by leveraging the symmetry of
*semi-metrics*. Note that the types of `SemiMetric` and
`Metric` do not completely follow the definition in mathematics as they do not require the "distance" to be able
to distinguish between points: for these types `x != y` does not imply
that `d(x, y) != 0` in general compared to the mathematical
definition of semi-metric and metric, as this property does not change
This type system has practical significance. For example, when computing pairwise distances
between a set of vectors, you may only perform computation for half of the pairs, derive the
values immediately for the remaining half by leveraging the symmetry of *semi-metrics*. Note
that the types of `SemiMetric` and `Metric` do not completely follow the definition in
mathematics as they do not require the "distance" to be able to distinguish between points:
for these types `x != y` does not imply that `d(x, y) != 0` in general compared to the
mathematical definition of semi-metric and metric, as this property does not change
computations in practice.

Each distance corresponds to a distance type. The type name and the corresponding mathematical definitions of the distances are listed in the following table.
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