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recursion definition recursion definition recursion is the process of repeating items in a self-similar way for instance when the surfaces of two mirrors are exactly parallel with each other the nested images that occur are a form of infinite recursion the term has a variety of meanings specific to a variety of disciplines ranging from linguistics to logic the most common application of recursion is in mathematics and computer science in which it refers to a method of defining functions in which the function being defined is applied within its own definition specifically this defines an infinite number of instances function values using a finite expression that for some instances may refer to other instances but in such a way that no loop or infinite chain of references can occur the term is also used more generally to describe a process of repeating objects in a self-similar way know more about solving recurrence relations tutorcircle.com page no 1/4

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example another interesting example is the set of all true reachable propositions in an axiomatic system if a proposition is an axiom it is a true reachable proposition if a proposition can be obtained from true reachable propositions by means of inference rules it is a true reachable proposition the set of true reachable propositions is the smallest set of propositions satisfying these conditions this set is called true reachable propositions because in non-constructive approaches to the foundations of mathematics the set of true propositions may be larger than the set recursively constructed from the axioms and rules of inference see also gödel s incompleteness theorems functional recursion a function may be partly defined in terms of itself a familiar example is the fibonacci number sequence fn fn 1 fn 2 for such a definition to be useful it must lead to values which are non-recursively defined in this case f0 0 and f1 1 a famous recursive function is the ackermann function which unlike the fibonacci sequence cannot easily be expressed without recursion proofs involving recursive definitions applying the standard technique of proof by cases to recursively-defined sets or functions as in the preceding sections yields structural induction a powerful generalization of mathematical induction which is widely used to derive proofs in mathematical logic and computer science learn more cone tutorcircle.com page no 2/4

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recursive optimization dynamic programming is an approach to optimization which restates a multiperiod or multistep optimization problem in recursive form the key result in dynamic programming is the bellman equation which writes the value of the optimization problem at an earlier time or earlier step in terms of its value at a later time or later step tutorcircle.com page no 3/4 page no 2/3

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thank you for watching presentation

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