[amitkgupta84]

I mean “valid” in the mathematical/logical sense. It does not follow from the stated assumptions that n > 1, in the inductive step is this proof.

This has nothing to do with the idea that it can be common practice to prove claims of the form for all n > N, P(n) by induction when N is a number like 4. Yes there is a perfectly valid way to use proof by induction to do such proofs. Has nothing to do with this blog post.

[shkkmo]

In a proof, you can absolutely assume something like "A is true", you do it as a part of a sub-proof. Then anything you prove in the sub-proof like "B is true" can be brought back into the main proof in the form: A implies B is true.

The blog post glosses over this assumption and thus ends up concluding "p(n) implies p(n+1)" instead of "p(n) implies (n>1 implies p(n+1))”