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Ordered field
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===Total order=== A [[Field (mathematics)|field]] <math>(F, +, \cdot\,)</math> together with a [[Total order#Strict total order|total order]] <math> \leq </math> on <math>F</math> is an '''{{visible anchor|ordered field}}''' if the order satisfies the following properties for all <math>a, b, c \in F:</math> * if <math>a \leq b</math> then <math>a + c \leq b + c,</math> and * if <math>0 \leq a</math> and <math>0 \leq b</math> then <math>0 \leq a \cdot b.</math> As usual, we write <math>a < b</math> for <math>a\le b </math> and <math>a\ne b</math>. The notations <math>b\ge a</math> and <math>b> a</math> stand for <math>a\le b</math> and <math>a < b</math>, respectively. Elements <math>a\in F</math> with <math>a>0</math> are called positive.
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