if the intersection of a decreasing sequence of closed sets is non empty, does the diameter of the sets tends to zero? [closed]

in the converse of Cantor's intersection theorem we have the intersection of a decreasing sequence of closed sets with diameters tending to zero is nonempty, then the metric space is complete.What if we remove the condition that the diameters of the sets tending to zero, does the theorem still holds? OR is it true that if the intersection of a decreasing sequence of closed sets is non empty, the diameter of the sets always tends to zero? if yes, how to prove that? if no then help me to construct the counter example.