"Beginners" here mostly means "first-year undergraduates reading mathematics at the University of Cambridge". I can assure you that those people very seldom hav

"Beginners" here mostly means "first-year undergraduates reading mathematics at the University of Cambridge". I can assure you that those people very seldom have any trouble agreeing that "0.999... < 1" is false. [EDITED to insert the word "mostly"; I expect WTG wasn't thinking only of his and his colleagues' first-year students.]