Introduction to Probability, Second Edition, 2nd Edition

A

Math

A.1    Sets

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

– Georg Cantor

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 $x\in S$ indicates that x is an element or member of the set S (and $x\notin S$ 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.  $\left\{1,3,5,7,\dots \right\}$ is the set of all odd numbers;

2.  $ℝ$ is the set of all real numbers;

3.  $\left\{\text{Worf, Jack, Tobey}\right\}$ is the set of Joe’s cats;

4.  $\left[3,7\right]$ is the closed interval consisting of all real numbers between $3$ and $7$;

5.  $\left\{HH,HT,TH,TT\right\}$ is the set of ...