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Totally ordered set


In mathematics, a linear order, total order, simple order, or (non-strict) ordering is a binary relation on some set , which is antisymmetric, transitive, and total (this relation is denoted here by infix ). A set paired with a total order is called a totally ordered set, a linearly ordered set, a simply ordered set, or a chain.

If is totally ordered under , then the following statements hold for all and in :


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