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, *I*_{1}, being considered less than another, *I*_{2}, if *I*_{1} is completely to the left of *I*_{2}. 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 .

An interval order defined by unit intervals is a semiorder.

The complement of the comparability graph of an interval order (, ≤) is the interval graph .

Interval orders should not be confused with the interval-containment orders, which are the containment orders on intervals on the real line (equivalently, the orders of dimension ≤ 2).

Read more about Interval Order: Interval Dimension

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**Interval Order**- Interval Dimension

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### Famous quotes containing the words order and/or interval:

“However fiercely opposed one may be to the present *order*, an old respect for the idea of *order* itself often prevents people from distinguishing between *order* and those who stand for *order*, and leads them in practise to respect individuals under the pretext of respecting *order* itself.”

—Antonin Artaud (1896–1948)

“The yearning for an afterlife is the opposite of selfish: it is love and praise for the world that we are privileged, in this complex *interval* of light, to witness and experience.”

—John Updike (b. 1932)