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!)

There are two axioms that need to be satisfied:

iff

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

.

Then

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