probably, when a stronger lens will be put in the microscope, physicists will be able to see that the object that seemed to be one dot with the new lens can be viewed as, e.g., two dots.

Note that both results (one dot and two dots) correctly represent the reality with the accuracy of the chosen instrument of the observation (lens). Physicists decide the level of the precision they need and obtain a result depending of the chosen level of the accuracy. In the moment when they put a lens in the microscope, they have decided the minimal (and the maximal) size of objects that they will be able to observe. If they need a more precise or a more rough answer, they change the lens of their microscope.

Analogously, when mathematicians have decided which mathematical languages (in particular, which numeral systems) they will use in their work, they have decided which mathematical objects they will be able to observe and to describe.

In natural sciences there always exists the triad – the researcher, the object of investigation, and tools used to observe the object – and the instrument used to observe the object bounds and influences results of observations. 