Show that in for all . I should clarify some notation here means the open ball with center 0, and radius 1.
Definition of norms:
;
My attempt:
I know that to show they are subsets of each other, I have to show the implication as well and next as well.
So I have, let , then , I just don't see how this would imply or
And I'm also unsure as to how to show .
Hints?