Linked from

The 47 pages that link to Natural number, each with the reason it gives.

• IntegerNarrower topic: Positive integers extend the counting numbers by adding zero and negative values.

• Set theoryBroader topic: In set-theoretic foundations, natural numbers can be constructed from sets.

• Mathematical inductionNarrower topic: The cases covered by induction are indexed by natural numbers.

• Zermelo–Fraenkel set theoryBroader topic: The Infinity axiom supports constructing the natural numbers within the theory.

• SequenceRelated: Natural numbers serve as the positions that index sequence terms.

• ZeroNarrower topic: Whether zero belongs to the counting numbers depends on how this broader set is defined.

• Ordinal numberNarrower topic: Finite ordinal positions are represented by natural numbers.

• CardinalityRelated: Their cardinality is the standard smallest infinite size.

• Cauchy criterionRelated: The index bound in the criterion controls how far along the sequence terms must be.

• Gödel numberingRelated: Each coded symbol, formula, or sequence receives a natural-number representation.

• Richard DedekindNarrower topic: His axiomatization treats natural numbers as a simply infinite system.

• Countable setRelated: Natural numbers serve as the indices for an enumeration.

• Finite setRelated: Finite cardinalities are natural numbers, so conventions about zero affect the definition.

• Positional notationRelated: Positional numerals commonly begin by representing counting numbers.

• Limit of a sequenceRelated: The cutoff in the convergence definition is an index chosen among the natural numbers.

• Computable functionRelated: Computability theory often encodes inputs and outputs as natural numbers.

• Cantor's diagonal argumentRelated: Natural numbers index the entries in a proposed enumeration.

• Total orderRelated: The usual numerical order gives a familiar total order on natural numbers.

• Sieve of EratosthenesNarrower topic: The sieve operates on a finite sequence of natural numbers starting above one.

• Cardinal numberRelated: The natural numbers provide the standard representative of countable infinity.

• ElementBroader topic: Natural numbers can be treated as elements of sets such as the integers.

• Infinite setBroader topic: They form the standard example of a countably infinite set.

• Least elementRelated: Under the usual order, the set has a least element: zero or one, depending on convention.

• OneNarrower topic: One is the first positive member of the natural-number sequence.

• ArithmeticRelated: Natural numbers provide the basic counting quantities on which elementary arithmetic is built.

• Convergent sequenceRelated: The phrase “eventually” means that a property holds at every index after some natural-number index.

• Presburger arithmeticRelated: These are the objects over which Presburger formulas are interpreted.

• SubtractionNarrower topic: Counting numbers are the simplest quantities commonly subtracted.

• Uncountable setBroader topic: Uncountability is defined by failure to match this set in a bijection.

• Archimedean propertyRelated: Natural-number multiples provide the repeated additions used in the defining comparison.

• Peano axiomsNarrower topic: The axioms characterize this number system.

• Axiom of infinityBroader topic: The axiom ensures a set large enough to contain every finite successor stage.

• Even numberBroader topic: Even natural numbers are one restricted part of the even integers.

• Primitive recursive functionNarrower topic: These functions take natural numbers as inputs and return natural numbers.

• Unary numeral systemRelated: Unary most directly represents natural-number quantities through their mark counts.

• Giuseppe PeanoRelated: The objects characterized by Peano’s axioms are the natural numbers.

• Infinite descentNarrower topic: The method relies on the natural numbers having no infinite strictly decreasing sequence.

• Triangular numberNarrower topic: The index n and the row sizes are natural numbers.

• ConstructivismRelated: Their inductive construction provides a basic model of mathematical objects built step by step.

• Number (mathematics)Broader topic: Natural numbers provide the basic counting numbers from which broader systems are developed.

• Paris–Harrington theoremRelated: The unprovability result concerns a statement formalized in arithmetic about these numbers.

• CodeNarrower topic: Natural numbers are the usual target objects for codes.

• Axiom of Empty SetBroader topic: In the von Neumann construction, zero is identified with the empty set.

• 0 (number)Related: Whether zero belongs to the natural numbers depends on the convention being used.

• Element of a setBroader topic: Natural numbers provide familiar objects whose membership in number sets can be tested.

• Greatest element and least elementRelated: Under the usual order, the natural numbers have a least element but no greatest element.

• Number (identifier)Compared with: An identifier may look like a natural number but does not express a count.