Editing Real coordinate space (section)

=== Affine space ===
{{details|Affine space}}
{{math|'''R'''<sup>''n''</sup>}} understood as an affine space is the same space, where {{math|'''R'''<sup>''n''</sup>}} as a vector space [[Group action (mathematics)|acts]] by [[translation (geometry)|translations]]. Conversely, a vector has to be understood as a "[[displacement (vector)|difference]] between two points", usually illustrated by a directed [[line segment]] connecting two points. The distinction says that there is no [[canonical form|canonical]] choice of where the [[origin (mathematics)|origin]] should go in an affine {{mvar|n}}-space, because it can be translated anywhere.