From the previous post "Zero Error Small Piece Of Pi" dated 11 Jan 2023, that series for \(\pi\) has a zero correction at the infinite term, that means the infinite but one term represents \(\pi\) fully, and \(\pi\) is rational. Eventually.
Neither \(e\) nor \(\sqrt{2}\) share this. Both their descending series representations tend to zero at the infinite term but not quite zero.
A new kind of irrationality.
