I don't think the introductory paragraph of the Gibbs Phenomenon article is bad. Quite the contrary, I think it's well-written. The opening sentence in the Tayl

I don't think the introductory paragraph of the Gibbs Phenomenon article is bad. Quite the contrary, I think it's well-written. The opening sentence in the Taylor series article is terrible, though, but it's at least factually correct. True horror occurs when there is a major mistake. Incidentally, I encountered one such mistake just an hour ago. In the Encyclopedia of Mathematics published by Springer, there is an article entitled "Schur determinant lemma" (https://encyclopediaofmath.org/wiki/Schur_determinant_lemma https://encyclopediaofmath.org/wiki/Schur_determinant_lemma), which says that the determinant of a block matrix (in Matlab's notation) [P Q;R S] is det(PS-RQ). But this in general is wrong unless PR=RP. The result that "Schur determinant lemma" or "Schur determinant formula" refers to is actually det[P Q;R S]=det(P)det(R-SP^{-1}Q) (provided that P is invertible).