https://ja.wikipedia.org/wiki/%E9%A0%86%E5%BA%8F%E5%9E%8B 順序型（order type）とは、全順序集合同士の "形" を比較するために、その構造のみに注目することによって得られる概念である。 https://en.wikipedia.org/wiki/Order_type Order type
In mathematics, especially in set theory, two ordered sets X and Y are said to have the same order type if they are order isomorphic, that is, if there exists a bijection (each element matches exactly one in the other set) f： X→ Y such that both f and its inverse are monotonic (preserving orders of elements). In the special case when X is totally ordered, monotonicity of f implies monotonicity of its inverse.
For example, the set of integers and the set of even integers have the same order type, because the mapping n→ 2n is a bijection that preserves the order. But the set of integers and the set of rational numbers (with the standard ordering) do not have the same order type, because even though the sets are of the same size (they are both countably infinite), there is no order-preserving bijective mapping between them. To these two order types we may add two more: the set of positive integers (which has a least element), and that of negative integers (which has a greatest element). (引用終り) 以上
