[Koshkin]

One could argue, easily, that the real numbers are not, in fact, "real," either, that they are rather an abstraction needed to make any measures "commensurable." As far as the magnitude goes, for example, there may be physical limits on how small things can be. (By the same token, even large positive integers can easily be seen as unreal, if you consider a number that is greater than the total count of things in the universe.)