Totally Ordered Set

up:: Partially Ordered Set

A totally ordered set is a Partially Ordered Set $X$ with a partial order relation $\le$ such that any two points can be related to each other. That is,

$$\forall x,y\in X:(x\le y)\vee (y\le x)$$

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References

• Um Curso de Álgebra Linear, Flávio Ulhoa Coelho & Mary Lilian Lourenço. Editora EDUSP.