Recursion Discrete Math

Recursive Functions in Discrete Mathematics Understanding Self-Referential Functions Explore recursive functions, functions that call themselves within their definition. This guide explains the principles of recursion, its base case and recursive step, and provides examples illustrating how recursive functions solve problems by breaking them down into smaller, self-similar subproblems.

5.2. Recursion Recursion is arguably the most powerful tool for a computer scientist. It is used throughout theory and practice. Unfortunately, it is one of the more difficult concepts to understand in computer science. In this chapter we will examine recursion in the context of mathematics and computer science. We will use the principle of induction to make logical arguments and proofs

Instructor Is l Dillig, CS311H Discrete Mathematics Recursive De nitions 218 Recursive De nitions in Math IConsider the following sequence 13927 81 IThis sequence can be de nedrecursivelyas follows a0 1 an 3 an 1 IFirst part calledbase case second part calledrecursive step

A recursive function is a function that its value at any point can be calculated from the values of the function at some ious points. For example, suppose a

Recursively Defined Functions Most of the functions we have dealt with in previous chapters have been defined explicitly by a formula in terms of the variable. We can also define functions recursively in terms of the same function of a smaller variable. In this way, a recursive function quotbuildsquot on itself. A recursive definition has two parts Definition of the smallest argument usually f

Expandcollapse global hierarchy Home Bookshelves Combinatorics and Discrete Mathematics Applied Discrete Structures Doerr and Levasseur

8.1 Recursion Recursion in computer science and mathematics refers to the idea of describing the solution of a problem in terms of solutions to easier instances of the same problem. This concept applies to de nitions as well as to algorithms or programs. For example, inductive de nitions can be thought of as a recursive de nitions since they de ne more complex instances of a concept in terms

Mathematical induction is a technique that can be applied to prove the universal statements for sets of positive integers or their associated sequences.

Recursive De nitions We can use recursion to de ne functions, sequences, sets. Mathematical induction and strong induction can be used to prove results about recursively de ned sequences and functions. Structural induction is used to prove results about recursively de ned sets.

Recursion, simply put, is the process of describing an action in terms of itself. This may seem a bit strange to understand, but once it quotclicksquot it can be an extremely powerful way of expressing certain ideas. Let's look at some examples to make things clearer.