From my explanations of the set theory to my daughter yesterday.
A set is a container, an empty string (ε or nothing) is an element. A set with nothing inside is not empty, because there is nothing inside. A set is empty (∅) if it does not have anything inside.
$ python >>> nothing='' >>> set=[nothing] >>> set [''] >>> set.append('') >>> set ['', ''] >>> set.remove('') >>> set [''] >>> set.remove(nothing) >>> set  >>> emptyset= >>> emptyset 
Doing nothing and not doing anything are two different things.