English Dictionary

order type

名詞

(set theory) 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".

日本語の意味

集合論において、集合に付与された順序が順序保存全単射によって同値とされる同値類に属するという、集合の順序構造の性質を示す概念（順序型）

When comparing different linearly ordered sets, mathematicians often classify them by their order type to capture the structure preserved by order-preserving bijections.

異なる線型順序集合を比較するとき、数学者はしばしば順序同型類によってそれらを分類し、順序を保つ全単射によって保持される構造を捉えます。

意味（1）

(set theory) 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".

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.

order types （ plural ）