Then, could we say that the general or abstract form of the ellipse is a set of vectors? And with that set, there is an identity element, namely the unit ball. And that the identity is what produces the uninteresting basis vectors. Maybe what makes the vector space (that is, the set of vectors) interesting is equipped linear operators on all the vector space's elements?
Maybe this whole structure, a set equipped with some operations, has distinguishable features. Or maybe it can perform as underlying machinery for practical endeavors.
Maybe this whole structure, a set equipped with some operations, has distinguishable features. Or maybe it can perform as underlying machinery for practical endeavors.