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.
In python:
$ 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.
