Totally Ordered

In mathematics, a linear order, total order, simple order, or (non-strict) ordering is a binary relation (here denoted by infix ≤) on some set X which is transitive, antisymmetric, and total. 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 X is totally ordered under ≤, then the following statements hold for all a, b and c in X: If a ≤ b and b ≤ a then a = b (antisymmetry); If a ≤ b and b ≤ c then a ≤ c (transitivity); a ≤ b or b ≤ a (totality).Antisymmetry eliminates uncertain cases when both a precedes b and b precedes a.
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