Probability and Random Processes
Chapter One
Sets, Fields, and Events
B 1.1 SET DEFINITIONS
The concept of sets play an important role in probability. We will define a set in the
following paragraph.
Definition of Set
A set is a collection of objects called elements. The elements of a set can also be sets.
Sets are usually represented by uppercase letters A, and elements are usually represented
by lowercase letters a. Thus
A = {[a.sub.1]; [a.sub.2]; ... , [a.sub.n]} (1.1.1)
will mean that the set A contains the elements [a.sub.1], [a.sub.2], ... , [a.sub.n].
Conversely, we can write that [a.sub.k] is an element of A as
[a.sub.k] [member of] A (1.1.2)
and [a.sub.k] is not an element of A as
[a.sub.k] [??] A (1.1.3)
A finite set contains a finite number of elements, for example, S = {2,4,6}. Infinite sets will
have either countably infinite elements suc ... read full excerpt from Probability and Random Processes ebook
