, i.e. those which possess every property possessed by 0 and by the successors of possessors, meaning by the "successor" of
the number
. Thus the class of "inductive numbers" is perfectly definite. By our general definition of cardinal numbers, the number of terms in the class of inductive numbers is to be defined as "all those classes that are similar to the class of inductive numbers"—i.e. this set of classes is the number of the inductive numbers according to our definitions.
Now it is easy to see that this number is not one of the inductive numbers. If
is any inductive number, the number of numbers from 0 to