 To this end, Wittgenstein demands (a) that a real number must be “compar[able] with any rational number taken at random” (i.e., “it can be established whether it is greater than, less than, or equal to a rational number” (PR §191)) and (b) that “[a] number must measure in and of itself” and if a ‘number’ “leaves it to the rationals, we have no need of it” (PR §191) (Frascolla 1980: 242–243; Shanker 1987: 186–192; Da Silva 1993: 93–94; Marion 1995a: 162, 164; Rodych 1999b, 281–291; Lampert 2009).