umarzein/wikipedia-headings-20k · Datasets at Hugging Face

upwards sequence	downwards sequence
[ "Set (mathematics)" ]	[ "History", "How sets are defined and set notation", "Membership", "The empty set", "Singleton sets", "Subsets", "Euler and Venn diagrams", "Special sets of numbers in mathematics", "Functions", "Cardinality", "Power sets", "Partitions", "Basic operations", "Applications", "Principle of inclusion and exclusion" ]
[ "Set (mathematics)", "History" ]	[ "Naive set theory", "Axiomatic set theory" ]
[ "Set (mathematics)", "History", "Naive set theory" ]	[]
[ "Set (mathematics)", "History", "Axiomatic set theory" ]	[]
[ "Set (mathematics)", "How sets are defined and set notation" ]	[ "Roster notation", "Semantic definition", "Set-builder notation", "Classifying methods of definition" ]
[ "Set (mathematics)", "How sets are defined and set notation", "Roster notation" ]	[ "Infinite sets in roster notation" ]
[ "Set (mathematics)", "How sets are defined and set notation", "Roster notation", "Infinite sets in roster notation" ]	[]
[ "Set (mathematics)", "How sets are defined and set notation", "Semantic definition" ]	[]
[ "Set (mathematics)", "How sets are defined and set notation", "Set-builder notation" ]	[]
[ "Set (mathematics)", "How sets are defined and set notation", "Classifying methods of definition" ]	[]
[ "Set (mathematics)", "Membership" ]	[]
[ "Set (mathematics)", "The empty set" ]	[]
[ "Set (mathematics)", "Singleton sets" ]	[]
[ "Set (mathematics)", "Subsets" ]	[]
[ "Set (mathematics)", "Euler and Venn diagrams" ]	[]
[ "Set (mathematics)", "Special sets of numbers in mathematics" ]	[]
[ "Set (mathematics)", "Functions" ]	[]
[ "Set (mathematics)", "Cardinality" ]	[ "Infinite sets and infinite cardinality", "The continuum hypothesis" ]
[ "Set (mathematics)", "Cardinality", "Infinite sets and infinite cardinality" ]	[]
[ "Set (mathematics)", "Cardinality", "The continuum hypothesis" ]	[]
[ "Set (mathematics)", "Power sets" ]	[]
[ "Set (mathematics)", "Partitions" ]	[]
[ "Set (mathematics)", "Basic operations" ]	[]
[ "Set (mathematics)", "Applications" ]	[]
[ "Set (mathematics)", "Principle of inclusion and exclusion" ]	[]
[ "Paradoxes of the Infinite" ]	[ "References" ]
[ "Paradoxes of the Infinite", "References" ]	[]
[ "Wikipedia, the free encyclopedia" ]	[]
[ "Mathematical object" ]	[ "List of mathematical objects by branch" ]
[ "Mathematical object", "List of mathematical objects by branch" ]	[]
[ "Ordered pair" ]	[ "Generalities", "Informal and formal definitions", "Defining the ordered pair using set theory", "Category theory" ]
[ "Ordered pair", "Generalities" ]	[]
[ "Ordered pair", "Informal and formal definitions" ]	[]
[ "Ordered pair", "Defining the ordered pair using set theory" ]	[ "Wiener's definition", "Hausdorff's definition", "Kuratowski's definition", "Quine–Rosser definition", "Cantor–Frege definition", "Morse definition", "Axiomatic definition" ]
[ "Ordered pair", "Defining the ordered pair using set theory", "Wiener's definition" ]	[]
[ "Ordered pair", "Defining the ordered pair using set theory", "Hausdorff's definition" ]	[]
[ "Ordered pair", "Defining the ordered pair using set theory", "Kuratowski's definition" ]	[ "Variants", "Proving that definitions satisfy the characteristic property" ]
[ "Ordered pair", "Defining the ordered pair using set theory", "Kuratowski's definition", "Variants" ]	[]
[ "Ordered pair", "Defining the ordered pair using set theory", "Kuratowski's definition", "Proving that definitions satisfy the characteristic property" ]	[]
[ "Ordered pair", "Defining the ordered pair using set theory", "Quine–Rosser definition" ]	[]
[ "Ordered pair", "Defining the ordered pair using set theory", "Cantor–Frege definition" ]	[]
[ "Ordered pair", "Defining the ordered pair using set theory", "Morse definition" ]	[]
[ "Ordered pair", "Defining the ordered pair using set theory", "Axiomatic definition" ]	[]
[ "Ordered pair", "Category theory" ]	[]
[ "Naive set theory" ]	[ "Method", "Sets, membership and equality", "Specifying sets", "Subsets", "Universal sets and absolute complements", "Unions, intersections, and relative complements", "Ordered pairs and Cartesian products", "Some important sets", "Paradoxes in early set theory" ]
[ "Naive set theory", "Method" ]	[ "Paradoxes", "Cantor's theory", "Axiomatic theories", "Consistency", "Utility" ]
[ "Naive set theory", "Method", "Paradoxes" ]	[]
[ "Naive set theory", "Method", "Cantor's theory" ]	[]
[ "Naive set theory", "Method", "Axiomatic theories" ]	[]
[ "Naive set theory", "Method", "Consistency" ]	[]
[ "Naive set theory", "Method", "Utility" ]	[]
[ "Naive set theory", "Sets, membership and equality" ]	[ "Note on consistency", "Membership", "Equality", "Empty set" ]
[ "Naive set theory", "Sets, membership and equality", "Note on consistency" ]	[]
[ "Naive set theory", "Sets, membership and equality", "Membership" ]	[]
[ "Naive set theory", "Sets, membership and equality", "Equality" ]	[]
[ "Naive set theory", "Sets, membership and equality", "Empty set" ]	[]
[ "Naive set theory", "Specifying sets" ]	[]
[ "Naive set theory", "Subsets" ]	[]
[ "Naive set theory", "Universal sets and absolute complements" ]	[]
[ "Naive set theory", "Unions, intersections, and relative complements" ]	[]
[ "Naive set theory", "Ordered pairs and Cartesian products" ]	[]
[ "Naive set theory", "Some important sets" ]	[]
[ "Naive set theory", "Paradoxes in early set theory" ]	[]
[ "Rational number" ]	[ "Terminology", "Arithmetic", "Continued fraction representation", "Other representations", "Formal construction", "Properties", "Real numbers and topological properties", "p-adic numbers" ]
[ "Rational number", "Terminology" ]	[ "Etymology" ]
[ "Rational number", "Terminology", "Etymology" ]	[]
[ "Rational number", "Arithmetic" ]	[ "Irreducible fraction", "Embedding of integers", "Equality", "Ordering", "Addition", "Subtraction", "Multiplication", "Inverse", "Division", "Exponentiation to integer power" ]
[ "Rational number", "Arithmetic", "Irreducible fraction" ]	[]
[ "Rational number", "Arithmetic", "Embedding of integers" ]	[]
[ "Rational number", "Arithmetic", "Equality" ]	[]
[ "Rational number", "Arithmetic", "Ordering" ]	[]
[ "Rational number", "Arithmetic", "Addition" ]	[]
[ "Rational number", "Arithmetic", "Subtraction" ]	[]
[ "Rational number", "Arithmetic", "Multiplication" ]	[]
[ "Rational number", "Arithmetic", "Inverse" ]	[]
[ "Rational number", "Arithmetic", "Division" ]	[]
[ "Rational number", "Arithmetic", "Exponentiation to integer power" ]	[]
[ "Rational number", "Continued fraction representation" ]	[]
[ "Rational number", "Other representations" ]	[]
[ "Rational number", "Formal construction" ]	[]
[ "Rational number", "Properties" ]	[ "Countability" ]
[ "Rational number", "Properties", "Countability" ]	[]
[ "Rational number", "Real numbers and topological properties" ]	[]
[ "Rational number", "p-adic numbers" ]	[]
[ "Set theory" ]	[ "History", "Basic concepts and notation", "Ontology", "Formalized set theory", "Applications", "Areas of study", "Objections to set theory", "Set theory in mathematical education" ]
[ "Set theory", "History" ]	[]
[ "Set theory", "Basic concepts and notation" ]	[]
[ "Set theory", "Ontology" ]	[]
[ "Set theory", "Formalized set theory" ]	[]
[ "Set theory", "Applications" ]	[]
[ "Set theory", "Areas of study" ]	[ "Combinatorial set theory", "Descriptive set theory", "Fuzzy set theory", "Inner model theory", "Large cardinals", "Determinacy", "Forcing", "Cardinal invariants", "Set-theoretic topology" ]
[ "Set theory", "Areas of study", "Combinatorial set theory" ]	[]
[ "Set theory", "Areas of study", "Descriptive set theory" ]	[]
[ "Set theory", "Areas of study", "Fuzzy set theory" ]	[]
[ "Set theory", "Areas of study", "Inner model theory" ]	[]
[ "Set theory", "Areas of study", "Large cardinals" ]	[]
[ "Set theory", "Areas of study", "Determinacy" ]	[]
[ "Set theory", "Areas of study", "Forcing" ]	[]
[ "Set theory", "Areas of study", "Cardinal invariants" ]	[]
[ "Set theory", "Areas of study", "Set-theoretic topology" ]	[]

[ "Set (mathematics)" ]

[ "History", "How sets are defined and set notation", "Membership", "The empty set", "Singleton sets", "Subsets", "Euler and Venn diagrams", "Special sets of numbers in mathematics", "Functions", "Cardinality", "Power sets", "Partitions", "Basic operations", "Applications", "Principle of inclusion and exclusion" ]

[ "Set (mathematics)", "History" ]

[ "Naive set theory", "Axiomatic set theory" ]

[ "Set (mathematics)", "History", "Naive set theory" ]

[]

[ "Set (mathematics)", "History", "Axiomatic set theory" ]

[]

[ "Set (mathematics)", "How sets are defined and set notation" ]

[ "Roster notation", "Semantic definition", "Set-builder notation", "Classifying methods of definition" ]

[ "Set (mathematics)", "How sets are defined and set notation", "Roster notation" ]

[ "Infinite sets in roster notation" ]

[ "Set (mathematics)", "How sets are defined and set notation", "Roster notation", "Infinite sets in roster notation" ]

[]

[ "Set (mathematics)", "How sets are defined and set notation", "Semantic definition" ]

[]

[ "Set (mathematics)", "How sets are defined and set notation", "Set-builder notation" ]

[]

[ "Set (mathematics)", "How sets are defined and set notation", "Classifying methods of definition" ]

[]

[ "Set (mathematics)", "Membership" ]

[]

[ "Set (mathematics)", "The empty set" ]

[]

[ "Set (mathematics)", "Singleton sets" ]

[]

[ "Set (mathematics)", "Subsets" ]

[]

[ "Set (mathematics)", "Euler and Venn diagrams" ]

[]

[ "Set (mathematics)", "Special sets of numbers in mathematics" ]

[]

[ "Set (mathematics)", "Functions" ]

[]

[ "Set (mathematics)", "Cardinality" ]

[ "Infinite sets and infinite cardinality", "The continuum hypothesis" ]

[ "Set (mathematics)", "Cardinality", "Infinite sets and infinite cardinality" ]

[]

[ "Set (mathematics)", "Cardinality", "The continuum hypothesis" ]

[]

[ "Set (mathematics)", "Power sets" ]

[]

[ "Set (mathematics)", "Partitions" ]

[]

[ "Set (mathematics)", "Basic operations" ]

[]

[ "Set (mathematics)", "Applications" ]

[]

[ "Set (mathematics)", "Principle of inclusion and exclusion" ]

[]

[ "Paradoxes of the Infinite" ]

[ "References" ]

[ "Paradoxes of the Infinite", "References" ]

[]

[ "Wikipedia, the free encyclopedia" ]

[]

[ "Mathematical object" ]

[ "List of mathematical objects by branch" ]

[ "Mathematical object", "List of mathematical objects by branch" ]

[]

[ "Ordered pair" ]

[ "Generalities", "Informal and formal definitions", "Defining the ordered pair using set theory", "Category theory" ]

[ "Ordered pair", "Generalities" ]

[]

[ "Ordered pair", "Informal and formal definitions" ]

[]

[ "Ordered pair", "Defining the ordered pair using set theory" ]

[ "Wiener's definition", "Hausdorff's definition", "Kuratowski's definition", "Quine–Rosser definition", "Cantor–Frege definition", "Morse definition", "Axiomatic definition" ]

[ "Ordered pair", "Defining the ordered pair using set theory", "Wiener's definition" ]

[]

[ "Ordered pair", "Defining the ordered pair using set theory", "Hausdorff's definition" ]

[]

[ "Ordered pair", "Defining the ordered pair using set theory", "Kuratowski's definition" ]

[ "Variants", "Proving that definitions satisfy the characteristic property" ]

[ "Ordered pair", "Defining the ordered pair using set theory", "Kuratowski's definition", "Variants" ]

[]

[ "Ordered pair", "Defining the ordered pair using set theory", "Kuratowski's definition", "Proving that definitions satisfy the characteristic property" ]

[]

[ "Ordered pair", "Defining the ordered pair using set theory", "Quine–Rosser definition" ]

[]

[ "Ordered pair", "Defining the ordered pair using set theory", "Cantor–Frege definition" ]

[]

[ "Ordered pair", "Defining the ordered pair using set theory", "Morse definition" ]

[]

[ "Ordered pair", "Defining the ordered pair using set theory", "Axiomatic definition" ]

[]

[ "Ordered pair", "Category theory" ]

[]

[ "Naive set theory" ]

[ "Method", "Sets, membership and equality", "Specifying sets", "Subsets", "Universal sets and absolute complements", "Unions, intersections, and relative complements", "Ordered pairs and Cartesian products", "Some important sets", "Paradoxes in early set theory" ]

[ "Naive set theory", "Method" ]

[ "Paradoxes", "Cantor's theory", "Axiomatic theories", "Consistency", "Utility" ]

[ "Naive set theory", "Method", "Paradoxes" ]

[]

[ "Naive set theory", "Method", "Cantor's theory" ]

[]

[ "Naive set theory", "Method", "Axiomatic theories" ]

[]

[ "Naive set theory", "Method", "Consistency" ]

[]

[ "Naive set theory", "Method", "Utility" ]

[]

[ "Naive set theory", "Sets, membership and equality" ]

[ "Note on consistency", "Membership", "Equality", "Empty set" ]

[ "Naive set theory", "Sets, membership and equality", "Note on consistency" ]

[]

[ "Naive set theory", "Sets, membership and equality", "Membership" ]

[]

[ "Naive set theory", "Sets, membership and equality", "Equality" ]

[]

[ "Naive set theory", "Sets, membership and equality", "Empty set" ]

[]

[ "Naive set theory", "Specifying sets" ]

[]

[ "Naive set theory", "Subsets" ]

[]

[ "Naive set theory", "Universal sets and absolute complements" ]

[]

[ "Naive set theory", "Unions, intersections, and relative complements" ]

[]

[ "Naive set theory", "Ordered pairs and Cartesian products" ]

[]

[ "Naive set theory", "Some important sets" ]

[]

[ "Naive set theory", "Paradoxes in early set theory" ]

[]

[ "Rational number" ]

[ "Terminology", "Arithmetic", "Continued fraction representation", "Other representations", "Formal construction", "Properties", "Real numbers and topological properties", "p-adic numbers" ]

[ "Rational number", "Terminology" ]

[ "Etymology" ]

[ "Rational number", "Terminology", "Etymology" ]

[]

[ "Rational number", "Arithmetic" ]

[ "Irreducible fraction", "Embedding of integers", "Equality", "Ordering", "Addition", "Subtraction", "Multiplication", "Inverse", "Division", "Exponentiation to integer power" ]

[ "Rational number", "Arithmetic", "Irreducible fraction" ]

[]

[ "Rational number", "Arithmetic", "Embedding of integers" ]

[]

[ "Rational number", "Arithmetic", "Equality" ]

[]

[ "Rational number", "Arithmetic", "Ordering" ]

[]

[ "Rational number", "Arithmetic", "Addition" ]

[]

[ "Rational number", "Arithmetic", "Subtraction" ]

[]

[ "Rational number", "Arithmetic", "Multiplication" ]

[]

[ "Rational number", "Arithmetic", "Inverse" ]

[]

[ "Rational number", "Arithmetic", "Division" ]

[]

[ "Rational number", "Arithmetic", "Exponentiation to integer power" ]

[]

[ "Rational number", "Continued fraction representation" ]

[]

[ "Rational number", "Other representations" ]

[]

[ "Rational number", "Formal construction" ]

[]

[ "Rational number", "Properties" ]

[ "Countability" ]

[ "Rational number", "Properties", "Countability" ]

[]

[ "Rational number", "Real numbers and topological properties" ]

[]

[ "Rational number", "p-adic numbers" ]

[]

[ "Set theory" ]

[ "History", "Basic concepts and notation", "Ontology", "Formalized set theory", "Applications", "Areas of study", "Objections to set theory", "Set theory in mathematical education" ]

[ "Set theory", "History" ]

[]

[ "Set theory", "Basic concepts and notation" ]

[]

[ "Set theory", "Ontology" ]

[]

[ "Set theory", "Formalized set theory" ]

[]

[ "Set theory", "Applications" ]

[]

[ "Set theory", "Areas of study" ]

[ "Combinatorial set theory", "Descriptive set theory", "Fuzzy set theory", "Inner model theory", "Large cardinals", "Determinacy", "Forcing", "Cardinal invariants", "Set-theoretic topology" ]

[ "Set theory", "Areas of study", "Combinatorial set theory" ]

[]

[ "Set theory", "Areas of study", "Descriptive set theory" ]

[]

[ "Set theory", "Areas of study", "Fuzzy set theory" ]

[]

[ "Set theory", "Areas of study", "Inner model theory" ]

[]

[ "Set theory", "Areas of study", "Large cardinals" ]

[]

[ "Set theory", "Areas of study", "Determinacy" ]

[]

[ "Set theory", "Areas of study", "Forcing" ]

[]

[ "Set theory", "Areas of study", "Cardinal invariants" ]

[]

[ "Set theory", "Areas of study", "Set-theoretic topology" ]

[]