> For the complete documentation index, see [llms.txt](https://mandober.gitbook.io/math-debrief/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mandober.gitbook.io/math-debrief/200-set-theory/topics/urelements.md).

# 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).