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Well-founded relation

In mathematics, a binary relation R is called well-founded (or wellfounded or foundational) on a set or, more generally, a class X if every non-empty subset (or subclass) S ⊆ X has a minimal element with respect to R; that is, there exists an m ∈ S such that for every s ∈ S, one does not have s R m. More formally, a relation is well-founded if: ( ∀ S ⊆ X…

Induction and recursion, Overview & Examples

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Induction and recursion

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Well-founded relation

Nodes55
Edges54
Triples28
Avg. degree1.96
Density0.036364
Components1

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Well-founded relation

Top relations

related to References · 12
Well-founded relation → American Mathematical Society ISBN, Discovering Modern Set Theory, Introduction, Just, Karel Hrbáček, Marcel Dekker ISBN, Martin, Set Theory, Thomas Jech, Weese, Well-founded, Winfried
related to Other properties · 5
Well-founded relation → Consider, If, Let, The Mostowski, Then
related to Reflexivity · 5
Well-founded relation → Every, For, In, More, To
related to Examples · 4
Well-founded relation → Every, The, This, Well-founded
is a · 1
Well-founded relation → usual ordering on the class of all ordinal numbers
related to Induction and recursion · 1
Well-founded relation → An

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well-founded relation set called element order induction every theory descending class relations numbers defined natural elements also usual finite implies

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SubjectPredicateObjectConfidenceSrc
Well-founded relationis ausual ordering on the class of all ordinal numbers0.90text
Well-founded relationrelated to ExamplesWell-founded0.60section
Well-founded relationrelated to ExamplesThe0.60section
Well-founded relationrelated to ExamplesEvery0.60section
Well-founded relationrelated to ExamplesThis0.60section
Well-founded relationrelated to Induction and recursionAn0.60section
Well-founded relationrelated to Other propertiesIf0.60section
Well-founded relationrelated to Other propertiesConsider0.60section
Well-founded relationrelated to Other propertiesLet0.60section
Well-founded relationrelated to Other propertiesThen0.60section
Well-founded relationrelated to Other propertiesThe Mostowski0.60section
Well-founded relationrelated to ReferencesJust0.60section

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