Theorem
Ifis a subset of
in a metric space
then
where
is the diameter of
Proof
Take
Supposethen
Choosesuch that
From the triangle inequality,
Henceso
Since
Hence
Theorem
Ifis a subset of
in a metric space
then
where
is the diameter of
Proof
Take
Supposethen
Choosesuch that
From the triangle inequality,
Henceso
Since
Hence