Eventual domination is a relation describing the asymptotic behavior of two functions. The function \(f\) is said to eventually dominate \(g\) if \(f(n) > g(n)\) for all sufficiently large \(n\). That is, \(f\) asymptotically outgrows \(g\). Over \(\mathbb{N} ightarrow \mathbb{N}\), eventual domination is transitive relation. It is not total, since we can construct two different functions such that neither eventually dominates the other. This relation is however antisymmetric, and extending the relation to "\(f(n)\) eventually dominates \(g(n)\) or \(f(n)=g(n)\)" gives rise to a partial order.