Is recursion used in the real world?

There is no recursion in the real-world. Recursion is a mathematical abstraction. You can model lots of things using recursion. In that sense, Fibonacci is absolutely real-world, as there are quite some real-world problems that can be modeled this way.
Accordingly, what kind of problems can recursion be used for?
Recursion is capable of breaking down large and complex problems into small problems. However, not every complex problem can be solved via Recursion. The use of the recursive function is most appropriate and effective for problems like iterative branching, such as sorting, traversing, binary search, and other data structures.
In respect to this, which is the base case of the recursion process? Finding the recursive steps. Recursion can be seen as a reduction from the bigger problem to the simplest, smallest instance of the same problem. The smallest of all sub-problems is called the base case. This is what we should find first. In the real world, your recursive process will often take the shape of a function.
Next, which is the best example of recursion in programming?
Recursion is a tool a programmer can use to invoke a function call on itself. Fibonacci sequence is the textbook example of how recursion is used. Most recursive code if not all can be expressed as iterative function, but its usually messy.
Just so, which is the smallest sub-problem in recursion?
The smallest of all sub-problems is called the base case. This is what we should find first. In the real world, your recursive process will often take the shape of a function.

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