  It is shown that properties of a discrete space-time geometry distinguish
from properties of the Riemannian space-time geometry. The discrete geometry is
a physical geometry, which is described completely by the world function. The
discrete geometry is nonaxiomatizable and multivariant. The equivalence
relation is intransitive in the discrete geometry. The particles are described
by world chains (broken lines with finite length of links), because in the
discrete space-time geometry there are no infinitesimal lengths. Motion of
particles is stochastic, and statistical description of them leads to the
Schr\"{o}dinger equation, if the elementary length of the discrete geometry
depends on the quantum constant in a proper way.
