$\Large\pi$ is Eventually Rational

 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.