A set is define a well define collection of distinct objects so why an empty set is called a set although it has no element?

Some time we have collection of zero objects and we call them empty sets. e.g. Set of natural numbers greater than 5 and less than 5. A = { x belongs to N / 5< x < 5 } Now see this is a set which have collection of elements which are greater than 5 and less than 5 ( from natural number).