Although set theory can be considered within a single first-order language, with only non- logical constant ∈, it is convenient to have more complicated languages, corresponding to the many …

In our first lecture on sets and set theory, we introduced a bunch of new symbols and terminology. This guide focuses on two of those symbols: ∈ and ⊆. These symbols represent concepts that, …

A partition of a set A is a choice of dividing the elements of A into pairwise disjoint nonempty subsets whose union is A. This sounds complicated but it just means we're dividing up the …

By a set, we mean any collection of objects, e.g., the set of all even integers, the set of all saxophone players in Brooklyn, etc. The objects which make up a set are called its members.

Suppose A is the set of students who loves CSE 191, and B is the set of students who live in the university dorm. A \ B : the set of students who love CSE 191 and live in the university dorm.

For infinite sets this can be tricky, so instead, you should use the technique of double set containment. If one is a subset of the other and vice versa, it can only be the case they are equal.

This work played an important role in the development of topology, and all the basics of the subject are cast in the language of set theory. However sets are not just a tool; like many other …