A partially ordered set 
is an interval order if it is isomorphic
to some set of intervals on the real
line ordered by left-to-right precedence. Formally, 
is an interval order provided that one can assign to each
an interval ![[x_L,x_R]](/images/equations/IntervalOrder/Inline4.svg)
such that 
in the real numbers iff 
in 
.
Interval Order
See also
Partially Ordered SetExplore with Wolfram|Alpha
References
Fishburn, P. C. Interval Orders and Interval Graphs: A Study of Partially Ordered Sets. New York: Wiley, 1985.Wiener, N. "A Contribution to the Theory of Relative Position." Proc. Cambridge Philos. Soc. 17, 441-449, 1914.Referenced on Wolfram|Alpha
Interval OrderCite this as:
Weisstein, Eric W. "Interval Order." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/IntervalOrder.html