Show that if $||\cdot||_1$, $||\cdot||_2$ are equivalent norms then $(V,||\cdot||_1)$ is a banach space iff $(V,||\cdot||_2)$ is. I really didn't get it. Of course both spaces are normed spaces but there are two things I don't understand:
Why is it so important to look at "Cauchy sequences"? Why can't I look at converging sequences? Aren't those equivalent?
If those are equivalent, ones a sequence converges to a limit (which is in the space) should it be different in the other "space", that is $(V,||\cdot||_2)?
I really didn't understand what I need to do here. I would truly appreciate your help.