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...

A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The...

Word-sense induction Backward induction in game theory and economics Induced representation, in representation theory Mathematical induction, a method...

the inductive reasoning other than deductive reasoning (such as mathematical induction), where the conclusion of a deductive argument is certain given...

Transfinite induction is an extension of mathematical induction to well-ordered sets, for example to sets of ordinal numbers or cardinal numbers. Its...

reasoning and mathematical logic dealing with proving mathematical theorems by computer programs. Automated reasoning over mathematical proof was a major...

symmetric functions of roots of equations", American Mathematical Monthly, 37 (7), Mathematical Association of America: 357–365, doi:10.2307/2299273,...

computer science, graph theory, and some other mathematical fields. It is a generalization of mathematical induction over natural numbers and can be further...

credited with the discovery of induction in 1831, and James Clerk Maxwell mathematically described it as Faraday's law of induction. Lenz's law describes the...

Euler–Maclaurin summation formula which can be formalized by mathematical induction, in which the induction step relies on integration by parts and on identities...

some proofs Gödel's completeness theorem and its original proof Mathematical induction and a proof Proof that 0.999... equals 1 Proof that 22/7 exceeds...

programming Mathematical induction Recursive data types Recursion Recursion (computer science) Structural induction Henkin, Leon (1960). "On Mathematical Induction"...

function – Result of repeatedly applying a mathematical function Mathematical induction – Form of mathematical proof Mise en abyme – Technique of placing...

good proof." Polya begins Volume I with a discussion on induction, not mathematical induction, but as a way of guessing new results. He shows how the...

ninth, final axiom is a second-order statement of the principle of mathematical induction over the natural numbers, which makes this formulation close to...

} The truth of de Moivre's theorem can be established by using mathematical induction for natural numbers, and extended to all integers from there. For...

efficient divide-and-conquer algorithms can be difficult. As in mathematical induction, it is often necessary to generalize the problem to make it amenable...

of concurrent interacting objects. Coinduction is the mathematical dual to structural induction.[citation needed] Coinductively defined data types are...

The history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. Before the modern...

by cases, proof by case analysis, complete induction or the brute force method, is a method of mathematical proof in which the statement to be proved is...

In set theory, ∈ {\displaystyle \in } -induction, also called epsilon-induction or set-induction, is a principle that can be used to prove that all sets...

cascade that could render parts of Earth orbit unusable Mathematical induction – Form of mathematical proof Placebo effect – Substance or treatment of no...

Peano Mathematical induction Structural induction Recursive definition Naive set theory Element (mathematics) Ur-element Singleton (mathematics) Simple...

electromagnetic induction from the magnetic field of the stator winding. An induction motor therefore needs no electrical connections to the rotor. An induction motor's...

apply mathematical induction and only well-known rules of arithmetic. Induction basis: For n = 1 the statement is true with equality. Induction hypothesis:...

Henkin, L. (1960). On mathematical induction. The American Mathematical Monthly. 67(4), 323-338. Henkin, L. (1961). Mathematical Induction. En MAA Film Manual...

recursive formula for a sequence of numbers a n {\displaystyle a_{n}} Mathematical induction, a method of proof also called "proof by recursion" Recursion, a...

color is a falsidical paradox that arises from a flawed use of mathematical induction to prove the statement All horses are the same color. There is no...

Bar induction is a reasoning principle used in intuitionistic mathematics, introduced by L. E. J. Brouwer. Bar induction's main use is the intuitionistic...

(also known as computability theory). Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their...