Re:All People in Canada are the Same Age (1997)
by MauranKilom on Sunday July 12, 2020 @07:16PM
(#23815550)
Please take a look at the principle of induction that is explained on that page.
In short: You fix k and assume that S(k) holds. If you can show that this always implies that S(k+1) holds, all you need is a base case (e.g. S(1) being true) to "recursively" prove that S(n) holds for all n >= 1 (or whatever your base case was).
Here the fault is that the induction step (proving S(k+1) from S(k)) requires k >= 2 but only specifically S(1) was proven.
In short: You fix k and assume that S(k) holds. If you can show that this always implies that S(k+1) holds, all you need is a base case (e.g. S(1) being true) to "recursively" prove that S(n) holds for all n >= 1 (or whatever your base case was).
Here the fault is that the induction step (proving S(k+1) from S(k)) requires k >= 2 but only specifically S(1) was proven.