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- Mathematical_induction abstract "Mathematical induction is a method of mathematical proof typically used to establish a given statement for all natural numbers. It is a form of direct proof, and it is done in two steps. The first step, known as the base case, is to prove the given statement for the first natural number. The second step, known as the inductive step, is to prove that the given statement for any one natural number implies the given statement for the next natural number. From these two steps, mathematical induction is the rule from which we infer that the given statement is established for all natural numbers.The method can be extended to prove statements about more general well-founded structures, such as trees; this generalization, known as structural induction, is used in mathematical logic and computer science. Mathematical induction in this extended sense is closely related to recursion. Mathematical induction, in some form, is the foundation of all correctness proofs for computer programs.Although its name may suggest otherwise, mathematical induction should not be misconstrued as a form of inductive reasoning (also see Problem of induction). Mathematical induction is an inference rule used in proofs. In mathematics, proofs including those using mathematical induction are examples of deductive reasoning, and inductive reasoning is excluded from proofs.".
- Mathematical_induction thumbnail Dominoeffect.png?width=300.
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- Mathematical_induction wikiPageWikiLink Addison-Wesley.
- Mathematical_induction wikiPageWikiLink Addition.
- Mathematical_induction wikiPageWikiLink Addition_of_natural_numbers.
- Mathematical_induction wikiPageWikiLink Al-Karaji.
- Mathematical_induction wikiPageWikiLink Arithmetic_progression.
- Mathematical_induction wikiPageWikiLink Arity.
- Mathematical_induction wikiPageWikiLink Associative_property.
- Mathematical_induction wikiPageWikiLink Associativity.
- Mathematical_induction wikiPageWikiLink Augustus_De_Morgan.
- Mathematical_induction wikiPageWikiLink Augustus_de_Morgan.
- Mathematical_induction wikiPageWikiLink Axiom.
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- Mathematical_induction wikiPageWikiLink Bhāskara_II.
- Mathematical_induction wikiPageWikiLink Binomial_theorem.
- Mathematical_induction wikiPageWikiLink Blaise_Pascal.
- Mathematical_induction wikiPageWikiLink Calculus.
- Mathematical_induction wikiPageWikiLink Category:Articles_containing_proofs.
- Mathematical_induction wikiPageWikiLink Category:Mathematical_induction.
- Mathematical_induction wikiPageWikiLink Chakravala_method.
- Mathematical_induction wikiPageWikiLink Charles_Sanders_Peirce.
- Mathematical_induction wikiPageWikiLink Combinatorial_proof.
- Mathematical_induction wikiPageWikiLink Combinatorics.
- Mathematical_induction wikiPageWikiLink Computer_science.
- Mathematical_induction wikiPageWikiLink Deductive_reasoning.
- Mathematical_induction wikiPageWikiLink Derivative.
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- Mathematical_induction wikiPageWikiLink Empty_product.
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- Mathematical_induction wikiPageWikiLink Euclid.
- Mathematical_induction wikiPageWikiLink Fermat.
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- Mathematical_induction wikiPageWikiLink First-order_logic.
- Mathematical_induction wikiPageWikiLink Francesco_Maurolico.
- Mathematical_induction wikiPageWikiLink George_Boole.
- Mathematical_induction wikiPageWikiLink Giuseppe_Peano.
- Mathematical_induction wikiPageWikiLink Golden_ratio.
- Mathematical_induction wikiPageWikiLink Inductive_reasoning.
- Mathematical_induction wikiPageWikiLink Inference_rule.
- Mathematical_induction wikiPageWikiLink Infinite_descending_chain.
- Mathematical_induction wikiPageWikiLink Infinite_descent.
- Mathematical_induction wikiPageWikiLink Jacob_Bernoulli.
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- Mathematical_induction wikiPageWikiLink List_of_logic_symbols.
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- Mathematical_induction wikiPageWikiLink Parmenides_(dialogue).
- Mathematical_induction wikiPageWikiLink Pascals_triangle.
- Mathematical_induction wikiPageWikiLink Peano_axioms.
- Mathematical_induction wikiPageWikiLink Pierre_de_Fermat.
- Mathematical_induction wikiPageWikiLink Plato.
- Mathematical_induction wikiPageWikiLink Prime_number.
- Mathematical_induction wikiPageWikiLink Problem_of_induction.
- Mathematical_induction wikiPageWikiLink Product_rule.
- Mathematical_induction wikiPageWikiLink Proof_by_infinite_descent.
- Mathematical_induction wikiPageWikiLink Proofs_involving_the_addition_of_natural_numbers.
- Mathematical_induction wikiPageWikiLink Q.E.D..
- Mathematical_induction wikiPageWikiLink Recursion.
- Mathematical_induction wikiPageWikiLink Recursion_(computer_science).
- Mathematical_induction wikiPageWikiLink Reflexive_relation.
- Mathematical_induction wikiPageWikiLink Richard_Dedekind.
- Mathematical_induction wikiPageWikiLink Rule_of_inference.
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- Mathematical_induction wikiPageWikiLink Set_theory.
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- Mathematical_induction wikiPageWikiLink Structural_induction.
- Mathematical_induction wikiPageWikiLink Table_of_logic_symbols.
- Mathematical_induction wikiPageWikiLink Topology.
- Mathematical_induction wikiPageWikiLink Transfinite_induction.
- Mathematical_induction wikiPageWikiLink Tree_(set_theory).
- Mathematical_induction wikiPageWikiLink Vacuous_truth.
- Mathematical_induction wikiPageWikiLink Well-founded.
- Mathematical_induction wikiPageWikiLink Well-founded_relation.
- Mathematical_induction wikiPageWikiLink Well-founded_set.
- Mathematical_induction wikiPageWikiLink Well-order.
- Mathematical_induction wikiPageWikiLink Well-ordered.
- Mathematical_induction wikiPageWikiLink File:Dominoeffect.png.
- Mathematical_induction wikiPageWikiLinkText "Induction axiom".
- Mathematical_induction wikiPageWikiLinkText "Induction".
- Mathematical_induction wikiPageWikiLinkText "Inductively".
- Mathematical_induction wikiPageWikiLinkText "Mathematical Induction".
- Mathematical_induction wikiPageWikiLinkText "Mathematical induction".
- Mathematical_induction wikiPageWikiLinkText "Mathematical induction#Axiom of induction".
- Mathematical_induction wikiPageWikiLinkText "Mathematical induction#Complete induction".
- Mathematical_induction wikiPageWikiLinkText "Mathematical induction#Complete_induction".
- Mathematical_induction wikiPageWikiLinkText "Mathematical induction#Induction on more than one counter".
- Mathematical_induction wikiPageWikiLinkText "Mathematical induction#base case".
- Mathematical_induction wikiPageWikiLinkText "Principle of Mathematical Induction".
- Mathematical_induction wikiPageWikiLinkText "Proof by induction".
- Mathematical_induction wikiPageWikiLinkText "Repeated applications".