A characterization of a mathematical object is a collection of properties that collectively distinguish that object from other similar objects. The object is said to be characterized by (or "determined by") the properties.

Some examples from Euclidean geometry:

Note that while the characterization itself is not unique (an infinite number of pairs of points can characterize the same straight line, for example), a given characterization must uniquely specify the intended object (two different straight lines cannot pass through the same two points).

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