Trying to prove that there exists a function f from natural numbers to positive real numbers, such that for every function g from natural numbers to nonnegative real numbers, g is either the big-oh of f or big-omega of f.
I have attempted to prove this through proof by contradiction but I'm having trouble generating a contradiction to show that for all functions f, there is a function g that is neither the big-oh or big-omega of f. I'd appreciate any help. Thanks!