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Uintell Mathematics Encyclopedia

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Trivially ordered set

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MathematicsFoundations and Logic

$A$ in which distinct elements are incomparable: $x \le y \Leftrightarrow x = y$. A trivial order has

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2020 Mathematics Subject Classification: Primary: 06A [MSN][ZBL]

A partially ordered set $A$ in which distinct elements are incomparable: $x \le y \Leftrightarrow x = y$. A trivial order has length zero.

How to Cite This Entry:
Trivial order. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Trivial_order&oldid=35420

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Foundations and LogicMathematics / Foundations and Logicmethod: field_fallback - confidence: 0.58suggested

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Trivially ordered setencyclopedia_of_mathematics Trivially ordered setencyclopedia_of_mathematics

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Partially ordered setoutgoing citation Lengthoutgoing citation Length of a partially ordered setincoming citation Ordered sumincoming citation

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discussesarticle:eom--trivial-order--dfd285f4b7 -> concept:trivially-ordered-setconfidence: 1.00 - provenance: encyclopedia_of_mathematicsconfirmed

discussesarticle:eom--trivially-ordered-set--f8b9839dc3 -> concept:trivially-ordered-setconfidence: 1.00 - provenance: encyclopedia_of_mathematicsconfirmed

citesconcept:trivially-ordered-set -> concept:partially-ordered-setconfidence: 1.00 - provenance: article link extractionreviewed

citesconcept:trivially-ordered-set -> concept:lengthconfidence: 1.00 - provenance: article link extractionreviewed

citesconcept:length-of-a-partially-ordered-set -> concept:trivially-ordered-setconfidence: 1.00 - provenance: article backlink extractionreviewed

citesconcept:ordered-sum -> concept:trivially-ordered-setconfidence: 1.00 - provenance: article backlink extractionreviewed

subcategory_ofconcept:trivially-ordered-set -> topic:foundations-and-logicconfidence: 0.58 - provenance: field_fallback classificationsuggested

Supported entity types include domain, subdomain, theory, concept, definition, theorem, conjecture, method, algorithm, problem, article, author, journal, dataset, and formal proof. The current import populates concepts, topics, articles, citations, source descriptions, and suggested classifications. Missing relation families are shown as empty instead of invented. See the Encyclopedia of Mathematics licensing notice.