a method can be defined recursively

Methods can call other methods ◇ Can a method call itself A recursive method is any method that calls itself Factorial numbers (i e , n) defined recursively:

be used to derive the method definition: – Subtask 1 is a smaller version of the original task, so it can be implemented with a recursive call – Subtask 2 is just the 

recursion • Examine recursive methods and unravel their processing steps Includes a base case that is defined directly It can be defined recursively:

When a function f(n), such as the ones in the previous examples, is defined recursively, the equation giving f(n + 1) in terms of previous values of f is called a recurrence relation Recursion: If n ∈ N, then n + 1 ∈ N Discussion There are a number of ways of defining the set N of natural numbers recursively

To prove that, we need a proof technique that allows us to prove statements that are true for all elements in a recursively defined set That technique is structural 

Functions defined recursively by themselves for novel computation paradigms Last but not is specified by using the void keyword for the function return type

Recursion is a programming technique in which a method can call itself to solve a problem ▻ A recursive definition is one which uses the word or concept being  

Recursion is a technique by which a method makes one or more calls to itself There is a natural recursive definition for the factorial function To see this,

Mathematical induction is a technique that can be applied to This process is called recursion Examples: • Recursive definition of an arithmetic sequence: