Let be points in
and define the distance between
and
by
Prove the following:
-
.
-
if and only if
.
-
.
- Proof. We compute,
- Proof. Assume
, then
Conversely, assume
. Then
for all
. Therefore,
- Proof. We compute
Let be points in
and define the distance between
and
by
Prove the following:
Conversely, assume . Then
for all
. Therefore,