Linked from

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

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

• 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.

• 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.

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

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

• 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.

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

• 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.

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

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

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

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