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# Order Isomorphic

Two totally ordered sets and are order isomorphic iff there is a bijection from to such that for all ,

(Ciesielski 1997, p. 38). In other words, and are equipollent ("the same size") and there is an order preserving mapping between the two.

Dauben (1990) and Suppes (1972) call this property "similar." The definition works equally well on partially ordered sets.

Avoided Pattern, Contained Pattern, Partially Ordered Set, Permutation Pattern, Totally Ordered Set

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## References

Ciesielski, K. Set Theory for the Working Mathematician. Cambridge, England: Cambridge University Press, 1997.Dauben, J. W. Georg Cantor: His Mathematics and Philosophy of the Infinite. Princeton, NJ: Princeton University Press, 1990.Mansour, T. "Permutations Avoiding a Pattern from and at Least Two Patterns from ." 31 Jul 2000. http://arxiv.org/abs/math.CO/0007194.Suppes, P. Axiomatic Set Theory. New York: Dover, 1972.

Order Isomorphic

## Cite this as:

Weisstein, Eric W. "Order Isomorphic." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/OrderIsomorphic.html