The Real Vector Spaces of Finite Sequences are Finite Dimensional

In this paper we show the finite dimensionality of real linear spaces with their carriers equal Rⁿ. We also give the standard basis of such spaces. For the set Rⁿ we introduce the concepts of linear manifold subsets and orthogonal subsets. The cardinality of orthonormal basis of discussed spaces is proved to equal n.

MML identifier: EUCLID 7, version: 7.11.01 4.117.1046