Why diameter of empty set is infinite give reasions?

The diameter of the empty set is considered to be infinite because there are no points within the set to define a finite distance. In mathematical terms, the diameter is defined as the supremum of the distances between all pairs of points in a set. Since the empty set has no pairs of points, the supremum is not defined in a finite sense, leading to the conclusion that it is infinite. This aligns with the idea that the empty set does not contain any measurable extent.