  In black hole physics, inflationary cosmology, and quantum field theories, it
is conjectured that the physical laws are subject to radical changes below the
Planck length. Such changes are due to effects of quantum gravity believed to
become significant at the Planck length. However, a complete and consistent
quantum theory of gravity is still missing, and candidate models of quantum
gravity have not yet overcome major formal and conceptual difficulties. Another
problem is how to determine a geometry of physical space that features a
minimal length scale such as the Planck length. In the present paper it is
demonstrated that the said geometry can be any geometric system omitting
continuity, i.e., a geometry that possesses only a finite number of points.
