Eventual domination

Eventual domination is a relation describing the asymptotic behavior of two functions. The function \(f\) is said to eventually dominate \(g\) iff \(f(n) > g(n)\) for all sufficiently large \(n\). That is, \(f\) asymptotically outgrows \(g\).

Theorems of the form "\(f\) eventually dominates every function with property \(P\)" are useful in formally giving a sense of scale for fast-growing functions, e.g. when property \(P\) means being provable in certain formal theory.