trichotomy law
law (every real number is either positive, negative, or zero)
Facts
6 properties- Instance of
- mathematical property
- Characteristic of
- set of real numbers
- Defining formula
- \forall x \in \mathbb{R} \, \forall y \in \mathbb{R} \, ( ( x < y \, \land \, \lnot (y < x) \, \land \, \lnot( x = y )\, ) \lor \, ( \lnot(x < y) \, \land \, y < x \, \land \, \lnot( x = y) \, ) \lor \, ( \lnot(x < y) \, \land \, \lnot( y < x) \, \land \, x = y \, \, ) )
- Described by source
- Dictionary.com
- Different from
- trichotomy
- Maintained by WikiProject
- WikiProject Mathematics
🏷️ Also known as
en trichotomy law
en trichotomy of the reals
en trichotomy of the real numbers
en axiom of trichotomy
en law of trichotomy
en trichotomy axiom
cs Trichotomická relace
de Gesetz der Trichotomie
el Νόμος της τριχοτομίας
es ley de tricotomia
es ley de tricotomía
fr trichotomie
it assioma della tricotomia
it legge della tricotomia
ja 三分律
ja 三分法 (数学)
pl relacja trychotomiczna
pt tricotomia
ru закон трихотомии
ru трихотомия (математика)
🔖 Identifiers · 5
- Encyclopædia Britannica Online ID
- topic/trichotomy-law
- Freebase ID
- /m/020szl
- MathWorld ID
- TrichotomyLaw
- Microsoft Academic ID (discontinued)
- 108963864
- PlanetMath ID
- LawOfTrichotomy
🔗 Connections
Characteristic of 1
Described by source 1
Instance of 1
Maintained by WikiProject 1
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Summary
trichotomy law is a mathematical property[1].
Key Facts
- Described by source: Dictionary.com[2]
- Different from: trichotomy[3]
- trichotomy law's defining formula is recorded as \forall x \in \mathbb{R} \, \forall y \in \mathbb{R} \, ( ( x < y \, \land \, \lnot (y < x) \, \land \, \lnot( x = y )\, ) \lor \, ( \lnot(x < y) \, \land \, y < x \, \land \, \lnot( x = y) \, ) \lor \, ( \lnot(x < y) \, \land \, \lnot( y < x) \, \land \, x = y \, \, ) )<sup id="cite-C6" class="cite-ref" title="trichotomy law — defining formula (P2534): \forall x \in \mathbb{R} \, \forall y \in \mathbb{R} \, ( ( x < y \, \land \, \lnot (y < x) \, \land \, \lnot( x = y )\, ) \lor \, ( \lnot(x < y) \, \land \,">[?].
- Maintained by WikiProject: WikiProject Mathematics[4]
- Characteristic of: set of real numbers[5]