Here's something which always manages to throw me in doubt. When one defines a function f to be greater than or equal to (or strictly greater) some other function g, So f >= g / f > g over some interval [a,b] simply speaking. Does this mean that for any value x in [a,b] : f(x) >= g(x)? OR f(x) >= g(y) , for any x in [a,b] and for any y in [a,b] ? Any insight will be highly appreciated, I'd like to clear this issue once and for all. Thank you very much!