Does it make any sense to talk about the dimension of a subset (not necessarily a subspace) of a vector space at all? What if say you can pick $n$ linearly independent vector from the subset but the set is not closed, then how do we call this number $n$? (Sorry, I know that my question maybe poorly worded, I hope you understand my meaning.) Thanks.
Definition clarification about dimension of a subset
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linear-algebra
vector-spaces