@MISC{Louvain_theeuclidean, author = {Université Catholique De Louvain}, title = {The Euclidean Space}, year = {} }

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Abstract

and [2] provide the notation and terminology for this paper. In the sequel k, n denote natural numbers and r denotes a real number. Let us consider n. The functor R n yields a non-empty set of finite sequences of � and is defined as follows: (Def.1) R n = � n. In the sequel x will denote a finite sequence of elements of �. The function | � | � from � into � is defined as follows: (Def.2) for every r holds | � | � (r) = |r|. Let us consider x. The functor |x | yields a finite sequence of elements of � and is defined as follows: (Def.3) |x | = | � | � · x. Let us consider n. The functor 〈0,...,0〉 yields a finite sequence of elements n of and is defined � by: