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In mathematics, the law of trichotomy states that every real number is either positive, negative, or zero. More generally, a binary relation R on a set X is trichotomous if for all x and y in X, exactly one of xRy, yRx and x = y holds. Writing R as <, this is stated in formal logic as:

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• Trichotomy (mathematics)
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• In mathematics, the law of trichotomy states that every real number is either positive, negative, or zero. More generally, a binary relation R on a set X is trichotomous if for all x and y in X, exactly one of xRy, yRx and x = y holds. Writing R as <, this is stated in formal logic as:
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• May 2018
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• In which axiomatization? Usually, the natural numbers N are introduced based on the Peano axioms, 'is less than' is defined recursively on N, and its trichotomy is proven by induction; integers, rationals, and reals are constructed step by step; again, trichotomy is proven for every of these domains.
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• In mathematics, the law of trichotomy states that every real number is either positive, negative, or zero. More generally, a binary relation R on a set X is trichotomous if for all x and y in X, exactly one of xRy, yRx and x = y holds. Writing R as <, this is stated in formal logic as:
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