Quote by bugatti79
Oh I see,
Axiom 1 <x,x> >=0 since we have that x_n for n=1,2,3 are in R

You're waving your arms here. Expand <x, x> using the definition of this inner product and it should be obvious why <x, x> >= 0.
Quote by bugatti79
Yes, the bar on top of them.
Anyway,
<y,x>=y1x1+y2x2+y3x3
=x1y1+x2y2+x3y3
=<x,y>
Is axiom 4 ok?
Thanks

Yes, #4 is fine.