Introduction to Probability

Appendix A

Math

A.1 Sets

A set is a Many that allows itself to be thought of as a One.

– Georg Cantor

Amazon should put their cloud in a cloud, so the cloud will have the redundancy of the cloud.

– @dowens

A set is a collection of objects. The objects can be anything: numbers, people, cats, courses, even other sets! The language of sets allows us to talk precisely about events. If S is a set, then the notation x ∈ S indicates that x is an element or member of the set S (and x ∉ S indicates that x is not in S). We can think of the set as a club, with precisely defined criteria for membership. For example:

1. {1, 3, 5, 7,...} is the set of all odd numbers;
2. {Worf, Jack, Tobey} is the set of Joe’s cats;
3. [3, 7] is the closed interval consisting ...