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...

some degree of probability. Unlike deductive reasoning (such as mathematical induction), where the conclusion is certain, given the premises are correct...

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

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

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

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

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

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

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

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

Natural induction can refer to: Mathematical induction Natural induction (labor) This disambiguation page lists articles associated with the title Natural...

In mathematics, a set is a collection of different things; these things are called elements or members of the set and are typically mathematical objects...

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...

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...

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...

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

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...

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...

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

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...

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

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

may be converted to for (i = 0; i < 10; ++i) { j = 1 << (i+1); } Mathematical induction Steven Muchnick; Muchnick and Associates (15 August 1997). Advanced...

'O' Level Mathematics and Additional Mathematics, depending on the school. Some topics covered in this course include mathematical induction, complex number...

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

} 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...

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

the graph of the successor function x ↦ x+1. Then induction on S is the usual mathematical induction, and recursion on S gives primitive recursion. If...

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

step. mathematical induction schema Synonym of mathematical induction. mathematical logic The study of logic within the framework of mathematical reasoning...