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Theorem

In mathematics and formal logic, a theorem is a statement that has been proven, or can be proven. The proof of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of the axioms and previously proved theorems.

Terminology, Theorems in logic & Theoremhood and truth

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Overview

Theoremhood and truth

Epistemological considerations

Informal account of theorems

Relation with scientific theories

Terminology

Layout

Lore

Theorems in logic

Citations

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Map overview Semantic statistics

Theorem

Nodes154
Edges153
Triples88
Avg. degree1.99
Density0.012987
Components1

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Theorem

Top relations

related to Terminology · 20
Theorem → An, BCE, Classical, Collatz, Conjectures, Conversely, Euclid's Elements, Fermat's Last Theorem, Gauss's, Goldbach's, Historically, In, Other, Over, Poincaré, Riemann, Sometimes, The, This, Zorn's
related to Theoremhood and truth · 13
Theorem → All, And, Euclid, Euclid's, Euclidean, For, In, One, Russell's, Similarly, These, This, Until
is a · 7
Theorem → logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of the axioms and previously proved theorems.In mains…, particularly well-known example of such a theorem, proved result that is not an immediate consequence of other known theorems, statement that has been proven, statement that has been proven to be true based on axioms and other theorems.A proposition is a theorem of lesser importance, theorem with a similar statement but a broader scope, well-formed formula of a mathematical theory that can be proved from the axioms and inference rules of the theory
related to Epistemological considerations · 7
Theorem → Although, English, However, In, Many, Namely, The
related to External links · 7
Theorem → Day, Eric, MathWorld, Media, Theorems, Wikimedia CommonsWeisstein, Wiktionary-logo-en-v2
related to Informal account of theorems · 7
Theorem → Alternatively, However, If, In, Logically, Such, The
related to Lore · 7
Theorem → Alfréd Rényi, Erdős, It, Paul Erdős, Rényi, Rényi's, The
related to Relation with scientific theories · 6
Theorem → Any, By, It, Mathematical, Nonetheless, Theorems
related to Theorems in logic · 5
Theorem → For, In, Some, The, Usually
related to Layout · 3
Theorem → In English, Paul Halmos, The

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Important terminology

theorems proof theory axioms logic mathematical true may proved also mathematics formal conjecture proposition example called statements statement proofs rules

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Theoremis astatement that has been proven0.90text
Theoremis alogical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of the axioms and previously proved theorems.In mains…0.90text
Theoremis aproved result that is not an immediate consequence of other known theorems0.90text
Theoremis awell-formed formula of a mathematical theory that can be proved from the axioms and inference rules of the theory0.90text
Theoremis aparticularly well-known example of such a theorem0.90text
Theoremis astatement that has been proven to be true based on axioms and other theorems.A proposition is a theorem of lesser importance0.90text
Theoremis atheorem with a similar statement but a broader scope0.90text
English for better readabilityinstance ofthey are often expressed informally in a natural language0.80text
Theoremrelated to Epistemological considerationsMany0.60section
Theoremrelated to Epistemological considerationsIn0.60section
Theoremrelated to Epistemological considerationsNamely0.60section
Theoremrelated to Epistemological considerationsHowever0.60section

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