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"