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If R is the set of all real numbers, what do the cartesian products R × R and R × R × R represent?

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The Cartesian product R × R represents the set R × R={(x, y) : x, y Î R}
which represents the coordinates of all the points in two dimensional space and the
cartesian product R × R × R represents the set R × R × R ={(x, y, z) : x, y, z Î R}
which represents the coordinates of all the points in three-dimensional space.

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