On Tuesday, 16 July 2013 21:23:32 UTC+2, Virgil wrote:
> Mathematical things are defined by definitions, at least
except most real numbers and most elements of larger sets.
> Thus WM claims that a non-terminating decimal, such as the one for 1/9, cannot be distinguished from any of its truncated thus terminating decimal approximations.
It can be distinguished from any of its terminating approximations, by its finite definition which allows to calculate every required digit, but that's always a that belongs to a finite initial segment.