Finite Normed Vectors form a Normed Vector Space

Last updated Nov 1, 2022

Let $V$ be a Vector Space and let $||\cdot||$ be an Extended Norm on $V$. Then $X \subset V$ defined as $$X := {x \in V : ||x|| < \infty}$$ is a Normed Vector Space.

TODO, this basically requires applying the Homogeniety and Triangle Inequality properties of an Extended Norm (Norm)