A recursive step — a set of rules that reduces all successive cases toward the base case. For example, the following is a recursive definition of a person's ancestor.
The process in which a function calls itself directly or indirectly is called recursion and the corresponding function is called a recursive function. A recursive algorithm takes one step toward solution and then recursively call itself to further move. The algorithm stops once we reach the solution.
Both place emphasis on breaking the problem down into smaller parts and solving the problem one step at a time, but the key difference is that recursive functions are usually partly defined by themselves.
The act of a function calling itself, recursion is used to solve problems that contain smaller sub-problems. A recursive function can receive two inputs: a base case (ends recursion) or a recursive case (resumes recursion).
In mathematics and computer science, a recursive definition, or inductive definition, is used to define the elements in a set in terms of other elements in the set (Aczel 1977:740ff).
Illustrated definition of Recursive: Applying a rule or formula to its own result, again and again. Example: start with 1 and apply double recursively:...
A function has to call itself at least once to be recursive, but eventually, it has to return the value you are looking for — otherwise it’s useless and will probably also result in the program crashing.