Hi. I have a question concerning mainly the idea of notation of dimensions. So we say that R2 is a 2 dimensional vector space. It can hold functions and vectors. The functions it holds are 1 dimensional like lines. And in R3 we can have two dimensional objects like planes. How about the vectors however. They are not functions, but do we say that in R2 we have 2 dimensional vectors and so on? So then how about for R1. Do we have 0 dimensional vectors? (points).So I am just asking about the notation for dimensions of vectors and functions in these vector spaces.
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A space an contain any object whose dimension is less than or equal to its own.
(R2 contains a plane, itself.) R1 can't contain any two dimensional objects, but can contain one dimensional objects(directed line segments) that can be thought of as vectors.