Conflicts in the Learning of Real Numbers and Limits.

The majority of students thought that 0.999 . . . was less than one. It may be that a few students had been taught using infinitesimal concepts, or that the phrase “just less than one” had connotations for the students different from those intended by the questioner; but it seems more likely that the answers represent the students’ own rationalisations made in an attempt to resolve conflicts inherent in the students’ previous experience of limiting processes.