Real n-space
In mathematics, real coordinate space of n dimensions, written Rn (/ɑːrˈɛn/ ar-EN) (also written ℝn with blackboard bold) is a coordinate space that allows several (n) real variables to be treated as a single variable. With various numbers of dimensions (sometimes unspecified), Rn is used in many areas of pure and applied mathematics, as well as in physics. With component-wise addition and scalar multiplication, it is the prototypical real vector space and is a frequently used representation of Euclidean n-space. Due to the latter fact, geometric metaphors are widely used for Rn, namely a plane for R2 and three-dimensional space for R3.
For any natural number n, the set Rn consists of all n-tuples of real numbers (R). It is called (the) "n-dimensional real space". Depending on its construction from n instances of the set R, it inherits some of the latter's structure, notably:
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