Talk:Principle of Mathematical Induction

Why are two variables (i.e n and k) needed? Why not just one? What is the advantage of utilizing k in step 2 below as opposed to n?

Suppose that:

$(1): \quad \map P {n_0}$ is true

$(2): \quad \forall n \in \Z: n \ge n_0 : \map P n \implies \map P {n + 1}$

Then:

$\map P n$ is true for all $n \in \Z$ such that $n \ge n_0$.

Thanks in advance! --Robkahn131 (talk) 13:46, 3 May 2021 (UTC)

I'd put it round the other way: what advantage does it give to use the same variable for the general statement as for the dummy variable? --prime mover (talk) 14:57, 3 May 2021 (UTC)