# Diameter of a non-empty set in a metric space

6. The diameter delta(A) of a non-empty set A in a metric space (X, d) is defined to be

delta(A) = sup [x, y BELONGING_TO A] d(x,y).

A is said to be bounded if delta(A) < infinity. Show that A SUBSET B implies delta(A) <= delta(B).

Please see the attached image for proper description of the question with appropriate symbols.

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#### Solution Summary

Diameter of a non-empty set in a metric space is clearly explored in this case.

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