  Science and mathematics help people better to understand world, eliminating
different fallacies and misconceptions. One of such misconception is related to
arithmetic, which is so important both for science and everyday life. People
think that their counting is governed by the rules of the conventional
arithmetic and that other kinds of arithmetic do not exist and cannot exist. It
is demonstrated in this paper that this popular image of the situation with
integer numbers is incorrect. In many situations, we have to utilize different
rules of counting and operating. This is a consequence of the existing
diversity in nature and society and to represent correctly this diversity
people have to utilize different arithmetics. To distinct them, we call the
conventional arithmetic Diophantine, while other arithmetics are called
non-Diophantine. Theory of non-Diophantine arithmetics is developed in the book
of the author "Non-Diophantine arithmetics or is it possible that 2 + 2 is not
equal to 4." In this work, some properties of non-Diophantine arithmetics are
considered, as well as their connections to numerical computations and
contemporary physics are explained.
