View source for Similar sets

A generalization of the elementary geometrical concept of a [[similarity]]. Two sets $A$ and $B$ that are [[totally ordered set|totally ordered]] by relations $R$ and $S$ respectively are said to be similar if there exists a [[bijection]] $f : A \rightarrow B$ such that for any $x,y \in A$ it follows from $x\, R\, y$ that $f(x)\, S\, f(y)$.



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An equivalence class of totally ordered sets under the relation of similarity is often called an ''[[order type]]''.

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