This is the principle of what is called “mathematical induction.”
It may be noticed that (iv) is the familar principle of mathematical induction.
We can ascend only by mathematical induction, which alone can teach us something new.
To all such numbers, proofs by mathematical induction can be validly applied.
A method of proof in which a statement is proved for one step in a process, and it is shown that if the statement holds for that step, it holds for the next.