Theorem
If
is a subset of
in a metric space
then
where
is the diameter of
Proof
Take
Suppose
then
Choose
such that
From the triangle inequality,
Hence
so
Since
Hence
Call Us 07766496223
Theorem
Ifis a subset ofin a metric spacethenwhereis the diameter of
Proof
Take
Supposethen
Choosesuch that
From the triangle inequality,
Henceso
Since
Hence