Transfinite Cardinal Numbers
In Chapter 18 a study was made of finite cardinal numbers. In that section it was assumed that finite sets have cardinal numbers and in particular the cardinal number of each set Nk is k. We chose to symbolize the expression, "the cardinal number of A," by #(A). In Chapter 18, after defining the finite cardinal numbers, operations for addition and multiplication were imposed on those numbers and properties such as commutativity and associativity were explored. Then the relation "<" was defined and some of its properties were considered. Now we will make a somewhat parallel investigation for infinite sets and their cardinal numbers. The reason for the word "somewhat" is that not all properties true of "=" and "<" in the finite context are true for cardinal numbers of infinite sets.