noun
Meaning 1
In 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".
Definition source: English Wiktionary via Wiktextract
Topics: mathematics, sciences, set-theory
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.
Meaning relationships
Synonyms: none provided
Antonyms: none provided