The empty set (denoted ;) is the set with no elements. There are a few symbols that are super helpful to know as a shorthand, and will be used throughout the course.

Sets are a useful vocabulary in many areas of mathematics. They provide a language for stating interesting results. For example, in analysis: “a monotone function from ‘ to ‘ is continuous except, at …

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 elements of A in …

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 …

Method 1: Roster Notation: A roster is a list of the elements in a set, separated by commas and surrounded by French curly braces.

Since we want to use theorems of set theory in doing model theory (and for other reasons concerning 220C), we adopt the following purely set theoretic definition as our official one.

Fundamental to set theory is the notion of membership; sets have members, also called elements. We write ‘aÎA’ to say that a is a member (element) of A, and we write ‘aÏA’ to say that a is not a member …