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ranging from linguistics to logic. The most common application of recursion is in mathematics and computer science, where a function being defined is applied...

Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory...

recursion is a method of solving a computational problem where the solution depends on solutions to smaller instances of the same problem. Recursion solves...

In mathematics and computer science, mutual recursion is a form of recursion where two mathematical or computational objects, such as functions or datatypes...

arithmetic also allows many techniques from recursion theory to be employed; many results in reverse mathematics have corresponding results in computable...

a_{n}} Mathematical induction, a method of proof also called "proof by recursion" Recursion, a 2004 science fiction novel by Tony Ballantyne Recursion (Crouch...

Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated...

In mathematics and computer science, iteration (along with the related technique of recursion) is a standard element of algorithms. In mathematics, iteration...

World of Mathematical Equations. Polyanin, Andrei D. "Difference and Functional Equations: Methods". at EqWorld - The World of Mathematical Equations...

chosen. More formally, we can state the Transfinite Recursion Theorem as follows: Transfinite Recursion Theorem (version 1). Given a class function G: V...

stellated polyhedra, originally as models for teaching. Mathematical concepts such as recursion and logical paradox can be seen in paintings by René Magritte...

In computability theory, Kleene's recursion theorems are a pair of fundamental results about the application of computable functions to their own descriptions...

Primitive recursion Ackermann function Raphael M. Robinson (1948). "Recursion and Double Recursion". Bulletin of the American Mathematical Society. 54...

and others, is best known as a founder of the branch of mathematical logic known as recursion theory, which subsequently helped to provide the foundations...

implementation of a mathematical function. In the lambda calculus there are a number of combinators (implementations) that satisfy the mathematical definition...

of mathematical induction over natural numbers and can be further generalized to arbitrary Noetherian induction. Structural recursion is a recursion method...

definitions had been used more or less formally in mathematics before, but the construction of primitive recursion is traced back to Richard Dedekind's theorem...

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

↦ x+1. Then induction on S is the usual mathematical induction, and recursion on S gives primitive recursion. If we consider the order relation (N, <)...

2, 3 etc. The recursion theorem states that such a definition indeed defines a function that is unique. The proof uses mathematical induction. An inductive...