Hi biddoggy!

a metric satisfies:

(1) d(x,x) = 0

and , if

So: ||x-x|| = ||0|| = 0

OKAY

||x-y|| > 0, because , thus

OKAY

(2) d(x,y) = d(y,x)

||x-y|| =||y-x||

||x-y|| = ||-(x-y)||

||x-y|| = |-1|*||x-y|

||x-y|| = ||x-y||

OKAY

(3)

||x+z - (y+z)|| \le ||x+z|| + ||-(y+z)|| = ||x+z|| + ||y+z||

OKAY

Are there any questions on that?

Yours

Rapha