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P-adic number

In number theory, given a prime number p, the p-adic numbers form an extension of the rational numbers that is distinct from the real numbers, though with some similar properties; p-adic numbers can be written in a form similar to (possibly infinite) decimals, but with digits based on a prime number p rather than ten, and extending to the left rather…

Applications, Definition & Algebraic closure

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Overview

Motivation

Informal description

Definition

Notation

P-adic expansion of rational numbers

P-adic integers

Topological properties

Modular properties

Cardinality

Algebraic closure

Multiplicative group

Local–global principle

Applications

Generalizations and related concepts

Advanced semantic analysis

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Map overview Semantic statistics

P-adic number

Nodes192
Edges191
Triples45
Avg. degree1.99
Density0.010417
Components1

How this topic connects Entity context

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P-adic number

Top relations

related to Generalizations and related concepts · 12
P-adic number → Cauchy, Completing, D/P, Dedekind, EP, If, It, Pick, Suppose, The, Therefore, This
related to Analysis · 8
P-adic number → Applications, Banach, Hahn, In, Similar, Some, The, Topological
related to External links · 6
P-adic number → Eric, Mathematics, MathWorld, Number, Springer On-line Encyclopaedia, Weisstein
related to Other equivalent definitions · 4
P-adic number → Modular, Other, Since, Topological
related to As equivalence classes · 3
P-adic number → Cauchy, It, The
related to Quantum physics · 3
P-adic number → Historically, This, Veneziano
related to Definition · 2
P-adic number → The, There
related to Local–global principle · 2
P-adic number → Helmut Hasse's, This
related to Topological properties · 2
P-adic number → The, This
has application · 1
P-adic number → The

Important terminology Word statistics

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Important terminology

p-adic displaystyle numbers series mathbb number integer field rational integers valuation tfrac one every modulo form example expansion infty absolute

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
P-adic numberhas applicationThe0.60section
P-adic numberrelated to AnalysisSimilar0.60section
P-adic numberrelated to AnalysisThe0.60section
P-adic numberrelated to AnalysisApplications0.60section
P-adic numberrelated to AnalysisSome0.60section
P-adic numberrelated to AnalysisIn0.60section
P-adic numberrelated to AnalysisTopological0.60section
P-adic numberrelated to AnalysisHahn0.60section
P-adic numberrelated to AnalysisBanach0.60section
P-adic numberrelated to As equivalence classesThe0.60section
P-adic numberrelated to As equivalence classesCauchy0.60section
P-adic numberrelated to As equivalence classesIt0.60section

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