In mathematics, especially order theory, the interval order for a collection of intervals on the real line is the partial order corresponding to their left-to-right precedence relation—one interval, I₁, being considered less than another, I₂, if I₁ is completely to the left of I₂. More formally, a poset  is an interval order if and only if there exists a bijection from to a set of real intervals, so , such that for any we have in exactly when . Such posets may be equivalently characterized as those with no induced subposet isomorphic to the pair of two element chains, the free posets .