Linked from

The 54 pages that link to Mathematical induction, each with the reason it gives.

• Natural numberRelated: Induction exploits the successor structure to prove statements across the sequence.

• FactorialRelated: The recurrence and base case give a natural inductive definition of factorial.

• Binomial theoremRelated: Induction extends the expansion from one exponent to every nonnegative integer exponent.

• Recurrence relationRelated: Induction often proves properties of sequences defined recursively.

• Fundamental theorem of arithmeticRelated: Induction proves that repeated prime extraction eventually factors every integer greater than 1.

• Richard DedekindRelated: Dedekind gave an influential axiomatic account of the natural numbers and induction.

• Empty setRelated: Recursive definitions often begin with an empty-set base case.

• Fibonacci sequenceRelated: Induction proves identities about all Fibonacci numbers from the recurrence.

• Finite setRelated: Induction proves many properties of finite sets by reducing them to smaller sizes.

• RecursionRelated: Its proof structure mirrors the base case and recursive step of many recursive definitions.

• Peano arithmeticRelated: The induction axiom schema lets the theory express that a property holding at zero and passing to successors holds universally.

• TheoremRelated: Induction establishes whole families of theorems about natural-number cases.

• Universal quantificationRelated: Its conclusion is universal, though the proof proceeds through a base case and successor step.

• Recreational mathematicsRelated: Inductive reasoning proves patterns in recursively defined puzzles and games.

• George PólyaRelated: Induction exemplifies the transition from noticing patterns to establishing a general result.

• Recursive definitionRelated: Its proof structure mirrors the base-and-step pattern of many recursive definitions.

• Algebraic identityRelated: Induction proves identities indexed by every natural number.

• Jordan–Hölder theoremRelated: A standard proof reduces the uniqueness claim to shorter series.

• Divide-and-conquer algorithmRelated: Its structure mirrors the base cases and recursive steps used to justify algorithms.

• Peano axiomsRelated: The induction principle is the axioms’ key rule for extending properties across the numbers.

• Even numberRelated: Induction often proves that recursively defined sequences remain even.

• Ramsey's theoremRelated: The classical proof extends the result from smaller subset sizes to larger ones.

• Van der Waerden's theoremRelated: Induction on progression length underlies a classic proof of the finite theorem.

• Bernoulli's inequalityRelated: Induction proves the inequality successively for nonnegative integer exponents.

• Giuseppe PeanoRelated: Peano formulated induction as a principle governing the natural numbers.

• Goodstein's theoremRelated: Peano arithmetic formalizes induction over natural numbers, but not every ordinal descent needed here.

• Mathematical conjectureRelated: Induction is a common route from verified initial cases to a general theorem.

• Mathematical puzzleRelated: Some puzzles become manageable by extending a pattern one step at a time.

• Paris–Harrington theoremRelated: Peano arithmetic includes induction, yet cannot prove the theorem.

• Pascal's ruleRelated: Induction uses the recurrence to prove formulas for entire rows or coefficient identities.

• Tower of HanoiRelated: Induction proves the recurrence gives the minimum number of moves for every disk count.

• Al-KarajiRelated: Al-Karaji used a form of induction in arguments about powers and sums.

• Discrete mathematicsRelated: Induction proves statements across the natural numbers and recursively defined structures.

• Hockey-stick identityRelated: Induction on the endpoint gives a direct proof using Pascal's rule.

• The Art of Computer ProgrammingRelated: Inductive proofs support the correctness arguments throughout the books.

• Fermat polygonal number theoremRelated: Inductive arguments help organize proofs across integers or polygonal orders.

• Lie's theoremRelated: Invariant subspaces let the triangularization proof pass from smaller representations to larger ones.

• Sperner's lemmaRelated: A common proof reduces the result in one dimension to the corresponding lower-dimensional case.

• Abel's binomial theoremRelated: Induction can verify the identity successively for all nonnegative integer exponents.

• Five color theoremRelated: Removing a low-degree vertex creates the smaller graph used in the proof.

• Shapiro inequalityRelated: Inductive proofs handle some odd-length cases by reducing them to shorter cyclic inequalities.

• Stolz–Cesàro theoremRelated: Induction often supports sequence inequalities used alongside the theorem.

• Zeckendorf's theoremRelated: Induction proves existence and uniqueness by reducing integers to smaller remainders.

• Balinski's theoremRelated: The standard proof uses dimension induction to establish connectivity.

• Cassini's identityRelated: Induction proves Cassini’s identity by propagating its alternating sign.

• Catalan–Mersenne conjectureRelated: The sequence's recursive definition makes induction natural for proving identities about its terms.

• Combinatorial principlesRelated: It proves counting formulas across all allowed sizes.

• Erdős–Nagy theoremRelated: Finite termination proofs often turn on showing a suitable quantity decreases.