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    Euclidean Space

    Alternate names

    Cartesian space | Euclidean n-space

    Basic definition

    Euclidean space of dimension n is the space of all n-tuples of real numbers which generalizes the two-dimensional plane and three-dimensional space.

    Detailed definition

    Euclidean n-space, sometimes called Cartesian space or simply n-space, is the space of all n-tuples of real numbers, (x_1, x_2, ..., x_n). Such n-tuples are sometimes called points, although other nomenclature may be used (see below). The totality of n-space is commonly denoted R^n, although older literature uses the symbol E^n (or actually, its non-doublestruck variant E^n; O'Neill 1966, p. 3).

    Related terms

    Euclidean plane | point | pseudo-Euclidean space | real line | real number | tensor | vector

    Educational grade level

    college level

    Associated person

    Euclid

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