An example of norms that are not equivalent

[Pyroadept]

Homework Statement

Give an example of two norms on a vector space that are not equivalent.

Homework Equations

The Attempt at a Solution

Hi everyone,

I know the definition for equivalent norms. I also know that norms on a finite dimensional vector space are equivalent. So clearly the vector space has to be infinitely dimensional.
In which case can you take the normal euclidean norm and the max norm? And if not, could someone please point me in the right direction?

Thanks for any help

 

[VeeEight]

Consider C[0,1] - continuous functions on the unit interval. Try the sup norm and L¹ norm.
Of course there are a lot of different examples, depending on what stuff you are comfortable with.