I am currently learning about vector spaces and have a slight confusion.
So I know that a vector space is a set of objects that are defined by addition and multiplication by scalar, and also a list of axioms.
I know that a subspace is created from the subset of a vector space and also defined by 3 properties (contain 0 vector, closed addition, closed multiplication by scalar).
Therefore, a vector space is also a subspace of itself. By this definition, every subspace of a vector space is a vector space.
From these definitions, can we say that all vector spaces are also subspaces? Especially since a vector space is a subspace of itself.