How do I approach inductive design problems with no information or context given? As a starting point for our course in Artificial Intelligence, we are being taught induction. We received a number of homework assignments where we have to show our inductive approach for a given problem.

An example of such a problem: "Sort an array of N numbers".

Reading through the course material and online sources I feel I have grasped the first concepts of induction. I have successfully proven some statements using induction, such as the number of steps for the Tower of Hanoi problem. However, I was able to prove it because I had some information beforehand, such as the number of steps required to move the tower in the form of a formula.

In the problems handed to us, we get a sentence like the one above and are asked: "Describe the inductive approach"

Should I select an arbitrary sorting algorithm, make my own assumptions and devise my own hypothesis and try to prove that? I just want to prove that the array is indeed sorted for any given number of N. What are some exemplary steps I could take in order to provide the inductive approach given that single sentence of "Sort an array of N elements"
Most questions in AI textbooks of this style are intended to be open ended so that the student can experiment on its own with the problem. So the golden rule is do as you see fit to provide the best learning!

In particular for this problem, your approach seems appropriate.

Since most sorting algorithms fall into a divide and conquer schema, you won't have problem fitting it into an inductive schema.

For example, you could take quicksort, which is usually implemented recursively. And then prove that it indeed sorts an array of size $n$ assuming that it sorts an array of size less than $n$.