On Fri, 17 Jun 1994, Jeff Gostin wrote:
Well, I don't know what it means. If you'd care to tell me, even in mail, I'd like to know. I've been following this thread with interest, but I don't pretend to follow this X(f(y)) notation all the time. I understand that it means we are applying function X to the result of f(y)... Anyone who's passed Trig or Elem. Functions does. I don't understand what function O(x) represents.
The way *I* learned it was like this: g(x) = o(f(x)) means that g(x)/f(x) -> 0 (as x goes to some specified limit) g(x) = O(f(x)) means that |g(x)/f(x)| is bounded (as x goes to some limit) In other words: a function that is o(f(x)) is of lower order than f(x), while a function that is O(f(x)) is of no higher order than f(x). - Sasha Volokh