"While the empty set is a standard and widely accepted mathematical concept, it remains an ontological curiosity, whose meaning and usefulness are debated by philosophers and logicians.

The empty set is not the same thing as nothing; rather, it is a set with nothing inside it and a set is always something. This can be a stumbling block. If so, the following homely figure of speech may be helpful. Think of a set as a bag, and its members as being the contents of the bag. An empty bag undoubtedly still exists."