Now I think I understand the subtlety, thanks! The induction part is important here because we start from n=1 (where the assumption is not as obviously question

Now I think I understand the subtlety, thanks! The induction part is important here because we start from n=1 (where the assumption is not as obviously questionable as for n in general, because it’s coincidentally/degeneratively true in relation to our reasoning) and then the “base error” allows us to generalize into a bigger mistake.