Research any topic before you write.

Find related topics. | Discover entities. | See connections. | Build a topical map.

Natural number

In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. The terms positive integers, non-negative integers, whole numbers, and counting numbers are also used. The set of the natural numbers is commonly denoted by a bold N or a blackboard bold ⁠ N {\displaystyle \mathbb {N} } ⁠.

History & Applications

Use the mouse wheel or two fingers (on touchscreens) to zoom in and out of the map.

Research this topic

Explore the main themes, entities and connections around Natural number. Start with the topic map, then use the sections below for research and deeper semantic analysis.

Explore this topic

Start with a few of the strongest sections from the source topic. These are research directions, not a list of keywords you must use.

Topics to explore

Browse the full topic structure. Each item opens a new analysis centered on that subject.

Overview

Intuitive concept

Terminology and notation

Use of natural numbers

Formal definitions

Properties

History

Generalizations

Advanced semantic analysis

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

Map overview Semantic statistics

Natural number

Nodes118
Edges117
Triples133
Avg. degree1.98
Density0.016949
Components1

How this topic connects Entity context

See the strongest relationship patterns around the current topic before diving into the raw triples.

Natural number

Top relations

related to Zero as natural number · 17
Natural number → Bernard Le Bovier, Bertrand Russell, Fontenelle, George, Giuseppe Peano, In, Including, ISO, John Horton Conway, Most, N0, N1, Nicolas Bourbaki, Paul Halmos, Starting, Stephen Cole Kleene, Wentworth
related to Formal construction · 9
Natural number → Europe, God, Henri Poincaré, Hermann Grassmann, In, Later, Leopold Kronecker, Peano's, The
related to Set-theoretic definition · 9
Natural number → By, Call, Define, In, John, Neumann, Such, The, This
see also · 9
Natural number → Axiom, Canonical, Function, Generalization, Mathematical, Mathematics, Representation, Set Theory, Size
related to Algebraic properties satisfied by the natural numbers · 8
Natural number → Associativity, Closure, Commutativity, Existence, However, If, No, The
related to Formal definitions · 8
Natural number → Every, Formal, Giuseppe Peano, In, Peano, The Peano, Two, While
related to Position in a sequence · 8
Natural number → But, Each, Every, For, More, The, They, This
related to history · 7
Natural number → Between, Encyclopaedia Britannica, English, For, Nicolas Chuquet, The, With
related to Addition · 6
Natural number → Given, In, Intuitively, It, The, This
related to Generalizations · 6
Natural number → Extensions, If, Number, Other, The, These

Important terminology Word statistics

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

numbers natural number set used displaystyle counting successor every defined axioms addition integers using called order mathbb objects multiplication peano

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
George Ainstance ofbut many mathematicians0.80text
Natural numberrelated to AdditionGiven0.60section
Natural numberrelated to AdditionIn0.60section
Natural numberrelated to AdditionIntuitively0.60section
Natural numberrelated to AdditionThe0.60section
Natural numberrelated to AdditionIt0.60section
Natural numberrelated to AdditionThis0.60section
Natural numberrelated to Algebraic properties satisfied by the natural numbersThe0.60section
Natural numberrelated to Algebraic properties satisfied by the natural numbersClosure0.60section
Natural numberrelated to Algebraic properties satisfied by the natural numbersAssociativity0.60section
Natural numberrelated to Algebraic properties satisfied by the natural numbersCommutativity0.60section
Natural numberrelated to Algebraic properties satisfied by the natural numbersExistence0.60section

Related concept clusters Concept neighborhoods

These clusters group vocabulary that occurs around closely connected concepts in the source material.

    Connections between topic areas Semantic bridges

    Bridges can reveal useful research angles that are easy to miss in a flat list of related terms.

    Min side: 3
    For writers, content strategists, SEOs, marketers and creators — from quick topic research to advanced semantic analysis.