  We first give a rigorous mathematical proof that classical mathematics
(involving such notions as infinitely small/large, continuity etc.) is a
special degenerate case of finite one in the formal limit when the
characteristic $p$ of the field or ring in finite mathematics goes to infinity.
We consider a finite quantum theory (FQT) based on finite mathematics and prove
that standard continuous quantum theory is a special case of FQT in the formal
limit $p\to\infty$. The description of states in standard quantum theory
contains a big redundancy of elements: the theory is based on real numbers
while with any desired accuracy the states can be described by using only
integers, i.e. rational and real numbers play only auxiliary role. Therefore,
in FQT infinities cannot exist in principle, FQT is based on a more fundamental
mathematics than standard quantum theory and the description of states in FQT
is much more thrifty than in standard quantum theory. Space and time are purely
classical notions and are not present in FQT at all. In the present paper we
discuss how classical equations of motions arise as a consequence of the fact
that $p$ changes, i.e. $p$ is the evolution parameter. It is shown that there
exist scenarios when classical equations of motion for cosmological
acceleration and gravity can be formulated exclusively in terms of quantum
quantities without using space, time and standard semiclassical approximation.
