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. ℵ_{0} is *not* a successor cardinal. But ℵ_{1} *is* a successor cardinal: it comes after ℵ_{0}. More generally, for any ordinal number k, ℵ_{k+1} is always a successor cardinal.