Why the word vector in vector space, and why the axioms are needed.
(I don't prove, but just state that the axioms are needed to write elements in V as column vectors of some basis (which I also don't prove that one will exist). And I provide examples to help that case.)
Work (unfinished):
Vector_space_basis.pdf
https://drive.google.com/file/d/1_qlSnzxKsZqqXZ2BaduU9Zn8dmODMLao/view?usp=sharing
VS_Basis_example.pdf (early handwritten, used E={[e, 1], [1, e]} )
https://drive.google.com/file/d/1Ya9vPpQumofPFjwR-0aGjuY-s1ZbHKJi/view?usp=sharing
Vector_Space_Axioms_props.pdf
https://drive.google.com/file/d/1YubQjNYRi6AM6TbM5RvnKxKXGyKnPOtB/view?usp=sharing
