There is no repetition in a set, meaning each element must be unique. You could, for example, have variations on an element, such as a regular number 4 and a boldface number 4.

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

It's used to indicate that something is an element of a set. So, in this example, we're using the symbol to indicate that the girl belongs to the set containing the boy and the girl. This statement is true because …

We now introduce Zermelo’s axioms for set theory. The axiom (or scheme) of separation tells us that whenever we separate the elements of a set into a subclass, the result is again a set.

There is only one set with no elements, named the empty set and denoted by the symbol ∅.

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.

Definitions Cardinal numbers: number of distinct elements in a set o Example: A = {1, 3, 5, 7} n(A) = 4 Complement of set A: set of all elements in the universal set that are not in A o Example: U = {1, 2, 3, …