Even if it's not meant to be true, I find it even more disturbing that the symbolic and English formulations doesn't seem to quite match up. (IMHO the symbolic formulation doesn't state that n must be integer.)
It's like the source code and comments being out of sync - you don't know which one is wrong.
Another great point.
I fixed the broken theorem, and I added a blurb on the "universe of discourse."
That may cost the author some of the readers for whom this text is the most educational, i.e. the ones that have trouble grasping the logic.