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Mathematical induction

Mathematical induction is a method for proving that a statement P ( n ) {\displaystyle P(n)} is true for every natural number n {\displaystyle n} , that is, that the infinitely many cases P ( 0 ) , P ( 1 ) , P ( 2 ) , P ( 3 ) , … {\displaystyle P(0),P(1),P(2),P(3),\dots } all hold. This is done by first proving a simple case, then also showing that if we…

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Examples

Variants

Example of error in the induction step

Formalization

Transfinite induction

Relationship to the well-ordering principle

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Mathematical induction

Nodes105
Edges104
Triples48
Avg. degree1.98
Density0.019048
Components1

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Mathematical induction

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related to history · 22
Mathematical induction → According, AD, Al-Samawal, Algebra, Bahir, BC, David, Euclid’s, Fabio Acerbi, Farmaki, Joyce, Karaji, Maghribi, Negrepontis, Pascal's, Plato, Plato’s Parmenides, Pythagoreans, The, The Brilliant
related to Infinite descent · 7
Mathematical induction → Because, Fermat, It, Its, Pierre, The, Using
related to Relationship to the well-ordering principle · 6
Mathematical induction → For, It, No, Peano, Suppose, The
related to Example of error in the induction step · 5
Mathematical induction → Base, Cohen, Joel, The, To
is a · 2
Mathematical induction → inference rule used in formal proofs, method for proving that a statement P
related to Description · 2
Mathematical induction → In, The
related to Prefix induction · 2
Mathematical induction → The, This
related to Sum of consecutive natural numbers · 2
Mathematical induction → Mathematical, This

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induction displaystyle natural statement case holds number step numbers proof prove mathematical base one true used principle hypothesis axiom cases

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SubjectPredicateObjectConfidenceSrc
Mathematical inductionis amethod for proving that a statement P0.90text
Mathematical inductionis ainference rule used in formal proofs0.90text
Mathematical inductionrelated to DescriptionThe0.60section
Mathematical inductionrelated to DescriptionIn0.60section
Mathematical inductionrelated to Example of error in the induction stepThe0.60section
Mathematical inductionrelated to Example of error in the induction stepTo0.60section
Mathematical inductionrelated to Example of error in the induction stepJoel0.60section
Mathematical inductionrelated to Example of error in the induction stepCohen0.60section
Mathematical inductionrelated to Example of error in the induction stepBase0.60section
Mathematical inductionrelated to historyAccording0.60section
Mathematical inductionrelated to historyDavid0.60section
Mathematical inductionrelated to historyJoyce0.60section

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