When there is a hierarchy $1 < 2 < ... < \aleph_0 < \aleph_1 < ...$ Can we say anything reasonable and useful about the ordering of the reciprocals of these numbers. To begin: $1/1 > 1/2 > 1/3$ makes sense, but I am not sure about the infinite ones. (For example, how should $1/\aleph_0$ compare with $1/\aleph_1$? I think there is something more to it than defining both of these things equal to 0.) Is there any research on this?
closed as not a real question by Simon Thomas, Franz Lemmermeyer, Gjergji Zaimi, Pete L. Clark, Robin Chapman Sep 12 2010 at 14:53