I think i've done this correctly, but i'm new to this module so I just want some confirmation that i've done it right (it's one of those modules where questions are unassessed so I could just be doing all the questions wrong!)For show that is not a metric on .
There are two axioms that need to be satisfied:
It satisfies the first axiom since gives and this is only possible if and .
I'm aiming to show that the second inequality does not hold.
I've decided to go with a proof by contradiction and try to contradict the first axiom.
So suppose .
So when we have so provided that and , we have that is not necessarily 0. This contradicts the first axiom.
Is this correct? After writing it down my proof by contradiction seems a bit odd =S