order type

plural order types · alternative order-type · alternative ordertype

1. mathematicsIn the context of sets equipped with an order (especially, the context of totally ordered sets), the characteristic of being a member of some equivalence class of such sets under the equivalence relation "existence of an order-preserving bijection".

   In [13] Chajoth studied how the order type of a chain can alter if we change the position of elements in a linearly ordered set, resp. if we introduce a new element in a linearly ordered set.

   2005, Egbert Harzheim, Ordered Sets, Springer, page 332

   2 more examples

   1965 [John Wiley], Raymond L. Wilder, Introduction to the Foundations of Mathematics: 2nd Edition, 2012, Dover, page 116, Another way of putting this is to state that the order type is that aspect of the arrangement of the elements of a simply ordered set, which remains unchanged when any two elements are exchanged. […] As in the case of cardinal numbers, order types may be denoted by suitable symbols called ordinal numerals.

   2011, Douglas Cenzer, Valentina Harizanov, Jeffrey B. Remmel, Effective Categoricity of Injection Structures, Benedikt Löwe, Dag Normann, Ivan Soskov, Alexandra Soskova (editors, Models of Computation in Context: 7th Conference on Computability in Europe, CiE 2011, Proceedings, Springer, LNCS 6735, page 51, We let ω denote the order type of N under the usual ordering and Z denote the order type of Z under the usual ordering.