[tomtomlapomme]

This is how induction proof work. You prove that something is true for a base (n = 1) case then you prove that if it is true for n it has to be true for n + 1. Therefore it is true for any n.

The flaw is that the second part of the proof requires n >= 2

[thwd]

I understand and agree but read carefully. The assumption _is_ the (entire) hypothesis. It is not existentially quantified or set in the base-case. It is the entire hypothesis.

[ashtonbaker]

You should read “n” as “some arbitrary n” in the quote you posted. It’s not an assumption for all n.

edit: sorry, you’re right that the wording is a bit sloppy. The “n” in the first quote is “for all n” and the n in the second quote is “some specific n” or “some arbitrary n”. They’re not meant to be the same statement. I don’t think it’s a very carefully written article.

[shkkmo]

The assumption that the case holds for n while the goal is to show the case holds for n+1. It is not well worded to make clear the intent of making an assumption about modal possibility. However, to see it as begging the question requires imposing a statement of modal necessity that simply isn't there.