Definitions:

A set is a container and its members (contents).

A sub-set is the container and some, or none, of its members.

Observations:

The empty set is the container. The container is a sub-set; a container is not a member of the set- an egg basket is not an egg.

It is the notion of container that distinquishes set from a collection or group of things. No eggs on the ground is an empty collection of eggs, which is trivial or meaningless. An empty egg basket has meaning.

If the container, such as an egg-basket, of a set is abstracted to “container,” the empty set is a subset of every set.*

Mathematical Definition of subset: U is a subset of S if every member of U is a menber of S, or equivalently, there are no members of U which are not members of S.

Does the mathematical definition hold up for the empty set? Yes: There are no members of the empty set which are not members of S. The empty set is a subset of S.

*EDIT: "the empty set is a subset of every set." is absoluteley wrong. I put correction in next post for emphasis, but thought I'd better correct it here too. The empty set (container) of integers is not the same as the empty set (egg basket) of eggs. You can't abstract the definition.