Understanding Norms: Why is f(0) = 0 Necessary?

[dirk_mec1]

Homework Statement

http://img221.imageshack.us/img221/605/61607025ge8.png


I don't see why f(0) = 0 is necessary for E to be a norm. And what does f(0) has to with f being differentible?

 

[Dick]

You didn't state your definition of norm. Does you definition include ||f||>0 if f is not 0? Think of the norm of a constant function.

 

[dirk_mec1]

http://img178.imageshack.us/img178/4205/91034874qm6.png

 

[Dick]

Fine. Check the 'definiteness' condition without the assumption f(0)=0.