ur-elements

Objects belonging to a set are called elements or members. They are distinct objects that make up that set. A set element may be a set itself.

If an element is not a set itself, it might be called an ur-element or atom. A set that contains only atoms may be called an atomic set. A set that only contains sets may be called a class. A proper class cannot be a member. t.

Additionally, as far as set theory is concerned only sets need exist, no other objects are necessary to derive further mathematical objects like numbers (to be examined later).