The standard definition of the number 0.999... is the limit of the sequence 0.9, 0.99, 0.999, ... A different definition involves what Terry Tao refers to as "ultralimit", i.e., the equivalence class [(0.9, 0.99, 0.999, ...)] of this sequence in the ultrapower construction, which is a number that falls short of 1 by an infinitesimal amount.
Študentsko zavračanje temelji na enem od nekaterih običajnih nepravilnih spoznav o realnih številih.