I was reading the Little Oh notation in a textbook. Apparently it has two meanings:

1) f(x) is Big-Oh (gx) which means f(x) <= g(x)

2) f(x) is NOT Big-Theta g(x)^4. (This definition confused me a lot.)

In my own words this would mean: f(x) <= g(x). Since Big Theta is Big Oh and Big Omega combined. f(x) is NOT <= g(x)^4 would mean f(x) is > g(x)^4 and f(x) is NOT >= g(x)^4 which mean f(x) is < g(x) ^ 4. Based on what I said, wouldn't the second definition actually mean f(x) is Big Theta g(x)^4?

Please correct me if I'm wrong.

**Edited by warnexus, 16 March 2013 - 09:30 AM.**