 After remarking that he has previously shown that all spaces \(G_n\) have the same power as the set of real numbers in the interval (0,1), and reiterating his conviction that any infinite point sets has either the power of the set of natural numbers or that of  (0,1),[32]  Cantor turns to the definition of the general concept of a continuum within \(G_{n}.\) For this he employs the concept of derivative or derived set of a point set introduced in a paper of 1872 on trigonometric series. Cantor had defined the derived set of a point set \(P\) to be the set of limit points of \(P,\) where a limit point of \(P\) is a point of \(P\) with infinitely many points of \(P\) arbitrarily close to it. A point set is called perfect if it coincides with its derived  set.[33]  Cantor observes that this condition does not suffice to characterize a continuum, since perfect sets can be constructed in the linear continuum which are dense in no interval, however small: as an example of such a set he offers the  set[34]  consisting of all real numbers in (0,1) whose ternary expansion does not contain a “1”.