Set

A set is a collection of different elements. In mathematics, they’re typically mathematical objects like numbers, symbols, points in space or other sets. A set can be finite or infinite. A set with no elements is called an empty set. A set with a single element is called a singleton.

Notation

To say that an element $x$ is in the set $A$, you can write it in the following way:

$$x\in A$$

To say that an element $x$ is not in a set A, it is written the following way:

$$x\notin A$$

Set-Building Notation

Set building notation is a way of describing a set that satisfies a certain predicate. It is written the following way:

$$\{x\in A|x<4\}$$

On the right side of the $|$ pipe character lies an expression that can evaluate to true or false (a predicate). If it satisfies the predicate on the right, it’s in the set on the left. If it doesn’t, it’s not.