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.

Explore with Wolfram|Alpha

More things to try:

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.

Referenced on Wolfram|Alpha

Order Isomorphic

Cite this as:

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

Order Isomorphic

See also

Explore with Wolfram|Alpha

References

Referenced on Wolfram|Alpha

Cite this as:

Subject classifications