Let's suppose without loss of generality
that ||*x*|| is no smaller than
||*y*||. (Otherwise we just interchange the roles
of *x* and *y*.)
Thus we have to show that

(*)

This follows directly from the triangle inequality itself if
we write *x* as

*x=x-y+y*

and think of it as

*x=(x-y) + y*.

Taking norms and
applying the triangle inequality gives

which implies (*).

Fine print, your comments, more links, Peter Alfeld, PA1UM.

[15-Mar-1998]