Exactly, the assumption (known as the inductive hypothesis) is completely fine by itself and doesn’t represent circular reasoning. The issue in the “proof” actually arises from the logic coming after this, in which they assume that they can form two differeny overlapping sets by removing a different horse from the total set of horses, which fails if n=2 (as then they each have a distinct element).
Comment on The science is divided
kogasa@programming.dev 15 hours agoNo, that’s what induction is. You prove the base case (e.g. n=1) and then prove that the (n+1) case follows from the (n) case. You may then conclude the result holds for all n, since we proved it holds for 1, which means it holds for 2, which means it holds for 3, and so on.
KingRandomGuy@lemmy.world 14 hours ago
sp3tr4l@lemmy.zip 14 hours ago
You are correct that in the mathematical sense, this is not circular reasoning, it is induction.
The problem is that this is an example of a failed, invalid proof of induction.
I investigated it a bit further and tried to work through the actual point at which the proof fails in another comment.