chapter  5
Cardinality
ByRavi P. Agarwal, Peter Cristina, O’Regan Donal
Pages 8

The sizes of finite sets can always be compared by counting the number of elements; however, this approach cannot be extended to infinite sets. A more effective approach which is applicable to finite as well as infinite sets to compare their sizes is to begin with a one-to-one correspondence (bijective mapping) between the elements of the given sets. This approach is particularly useful to realize how differently the elements of infinite sets are saturated. In particular, this will show us that there are many different sizes of infinite sets. We begin this chapter with the following definitions.