Let us take several values of n:

Thus, E1 is just the set of real numbers, or the real line.

Thus, E2 is the set of pairs of real numbers, or the Cartesian plane.

Thus, E3 is the set of triples of real numbers, or three-dimensional Euclidean space.

Thus, E4 is the set of quadruples of real numbers, or four-dimensional Euclidean space.

etc., etc.

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