A short technical comment on Bub's There is No Quantum World (arXiv:2512.18400v2) and a brief remark on related Grangier's reply (arXiv:2512.22965

This note is a friendly technical check of Jeffrey Bub’s There is No Quantum World (arXiv:2512.18400v2). I flag one unambiguous mathematical slip (a cardinality identity that implicitly assumes the Continuum Hypothesis) and then point out a few places where the discussion of infinite tensor products, ``sectorization,‘’ and measurement updates would benefit from sharper wording. Nothing here is meant as a critique of Bub’s interpretive goals; the aim is simply to separate what is mathematically forced from what depends on choices of algebra, representation, or philosophical stance. I end with a short remark on Philippe Grangier’s reply (arXiv:2512.22965v1).