  Every physical measuring needs a finite, different from zero measurement time
and provides information in form of the choice of a measurement result from all
possible measurement results. If infinitely many (different) measurement
results would be possible, the choice of a measurement result could deliver an
infinite quantity of information. But the results of physical measurings (of
finite duration) never deliver an infinite quantity of information, they
describe past, finite reality. Therefore the set of all possible measurement
results a priori is finite. In the physical reality only a finite information
quantity can be processed within a finite time interval. For mathematical
models whose representation requires a processing of an infinite quantity of
information, for example irrational numbers, no (exact) equivalent exists in
the physical reality. So mathematical calculations, which have an equivalent in
physical reality, can include only rational (finitely many elementary)
combinations of rational numbers. Conclusions arise from this for the
foundations of mathematical physics.
