in Misconceptions

Fallacious yet widespread and documented beliefs courtesy of Wikipedia.
Contrary to a widespread perception, the real number 0.999...—where the decimal point is followed by an infinite sequence of nines—is exactly equal to 1 by definition. They are two different ways of writing the same real number. A 2009 study by Weller et al. states that "Tall and Schwarzenberger (1978) asked first year university mathematics students whether 0.999... is equal to 1. The majority of the students thought that 0.999... is less than 1." Weller et al. go on to describe their own controlled experiment, performed "during the 2005 fall semester at a major research university in the southern United States. Pre-service elementary and middle school teachers from all five sections of a sophomore-level mathematics content course on number and operation participated in the study." The results are striking: "On the question of whether .999...=1, 72% of the control group and 83% of the experimental group expressed their view that .999... is not equal to 1."