Main Question or Discussion Point
A few weeks ago, I was rereading my multivariable calculus textbook, because I've recently studied linear algebra and hoped to more fully understand the subject. Anyway, I noticed that when discussing the epsilon-delta definition of limits, they defined it with respect to the standard L2 norm. Since one norm is as good as another, that got me thinking: can one use different norms to define different calculi? Or does it turn out that no matter what norm you pick, you end up with the same basic results?