Summary: Counting.
Whenever X is a set we let
|X|
be the number of members of X if X is finite and we let it be if X is infinite. Here are some basic counting
principles.
1. Unions. Suppose X is a disjointed family of finite sets. Then
(1) X =
XX
|X|.
For example, if m is a positive integer and X1, . . . , Xm are finite sets such that
(2) Xi Xj = whenever 1 i < j m
we can let X = {X1, . . . , Xm} and obtain
(3) |
m
i=1
Xi| =
m
i=1
|Xi|.
Even if (2) does not hold we have the inclusion-exclusion priciple

Source: Allard, William K. - Department of Mathematics, Duke University

Collections: Mathematics