Common · Knowledge
Order type
Two ordered sets X,Y are said to have the same order type just when they are order isomorphic, that is, when there exists a bijection f: X → Y such that both f and its inverse are strictly increasing
In mathematics, especially in set theory and order 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 pairs with exactly one in the other set) f : X → Y {\displaystyle f\colon X\to 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 already implies monotonicity of its inverse.
From Wikipedia
In mathematics, especially in set theory and order 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 pairs with exactly one in the other set) f : X → Y {\displaystyle f\colon X\to 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 already implies monotonicity of its inverse. One and the same set may be equipped with different orders. Since order-equivalence is an equivalence relation, it partitions the class of all ordered sets into equivalence classes.
Text: Wikipédia, CC BY-SA 4.0. ·
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