Hey,

Yes indeed I have tried myself. The following is what I have so far:

By definition I know that:

It is clear that:

Applying the definition in the beginning we have:

We conclude that the norm

does not satisfy the parallelogram law. My question is : "How does this show that the infinity-norm does not come from an inner-product? Is is simply because the above shows that the infinity-norm does not fulfill the parallelogram law which is one of the requirements for a vectorspace with an inner-product and associated norm?"

Thanks.