The fundamental operation on cardinal numbers is finding the next larger. A cardinal number l is called a successor cardinal if l is the next larger cardinal after k (l is the successor of k).

Every finite cardinal number apart from 0 is a successor cardinal. ℵ0 is not a successor cardinal. But ℵ1 is a successor cardinal: it comes after ℵ0. More generally, for any ordinal number k, ℵk+1 is always a successor cardinal.