What is the correct term for sets that dont contain other sets? As the title asks, what is the correct term for a set that don't contain another set?
I have called them "flat" but what is the correct term?
 A: I've not heard of any term for this in particular. But the term urelements is used for elements that are not sets, so you could call your set a set of urelements.
One warning though: As you can see by following that link, the standard ZF axioms of set theory are formulated in such a way that urelements do not exist, i.e. everything is a set, and therefore (as said in the comments) the only set whose elements are not sets is the empty set. The reason for this formulation is explained in that link: "the urelements were not needed because they can easily be modeled in a set theory without urelements."
One thing to keep in mind: in analysis or geometry, it is not of particular importance whether numbers are or are not sets. Nonetheless, when analysis and geometry are modelled using the standard ZF axioms of set theory, every number is a set, every geometric point is a set, and so on.
You might be interested, for example, in the Von Neumann definition of the natural numbers, which is formulated in set theory. And perhaps you already know how one can, within set theory, use the natural numbers to form the integers, the integers to form the rationals, and the rationals to form the reals. And, of course, one can use the reals to form the points of the Euclidean plane and so on.
