might both be the null-class.

Let us illustrate this possibility by an example: Suppose there were exactly nine individuals in the world. (As to what is meant by the word "individual," I must ask the reader to be patient.) Then the inductive cardinals from 0 up to 9 would be such as we expect, but 10 (defined as

) would be the null-class. It will be remembered that

may be defined as follows:

is the collection of all those classes which have a term