Problems related to the idea of infinity are among the most fundamental and have attracted the attention of the most brilliant thinkers throughout the whole history of humanity. Many eminent researchers from Archimedes and Euclid to Hilbert and Gödel worked hard on these topics (normal people become just crazy when start to think about). To emphasize the importance of the subject, it is sufficient to mention that the famous Continuum Hypothesis related to infinity has been included by David Hilbert as the problem number one in his famous list of 23 unsolved mathematical problems for the 20th century.

Traditional rules developed by mathematicians to work with infinite numbers are quite different with respect to the finite arithmetic we are used to deal with. They leave undetermined many operations where infinite numbers take part (for example, ∞-∞, ∞/∞, etc.) or use representation of infinite numbers based on infinite sequences of finite numbers. These crucial difficulties did not allow people to think about possibility to construct computers that would be able to work with infinite and infinitesimal numbers in the same manner as we are used to do with finite numbers.

The point of view on infinity accepted nowadays is based on the famous ideas of Georg Cantor who has shown that there exist infinite sets having different number of elements. However, it is well known that Cantor's approach leads to some "strange" results. For example, he has shown that the set Z = {… -3, -2, -1, 0, 1, 2, 3, …} of integer numbers has the same number of elements as the set N = {1, 2, 3, …} of natural numbers in spite of the fact that N is a part of Z.

If you remember your reaction when you have heard about at the first time, it was very difficult to accept this result because it is in an evident disagreement with the real world around us where the part is always less than the whole. But then you thought: "It should be so because the teacher tells us about. Probably, I am not sufficiently smart to understand this infinity stuff invented by all these wise guys." Thus, we all just trust our teachers and start to think that all these difficulties are related to the nature of infinite objects.

I have shown that problems related to infinite and infinitesimal objects are not intrinsic, characteristic features of the infinity but are just a consequence of the weakness of mathematical languages used to describe it. I have introduced a new powerful positional system with infinite base allowing one to write down in an explicit form not only usual finite but infinite and infinitesimal numbers too. In this new system, if you add a positive x to an y, you have x+y>x for any y: finite, infinite, and infinitesimal. I have overcome the difficulties of traditional views on infinity and created a simple and intuitive arithmetic that is (infinitely!) closer to the real world then the previous theories.

By using this highly innovative approach I have shown then that the new tools allow one to do things in calculus that nobody was able to do before. For example, it becomes possible to calculate sums of divergent series (e.g., the sum of all natural numbers!) and improper integrals of various types, and to execute operations being indeterminate forms in traditional approaches, e.g., difference and division of divergent series. One more example: it is now possible to evaluate functions and their derivatives at infinitesimal, finite, and infinite points and infinite and infinitesimal values of the functions and their derivatives can be also calculated.

How was I able to do this? Have a look at my popular book "Arithmetic of Infinity" where this stuff is described in a simple, easily understandable form, combining very successfully new deep ideas and a highly intuitive presentation demonstrating once again the truth of the words of Albert Einstein who said "Most of the fundamental ideas of science are essentially simple, and may, as a rule, be expressed in a language comprehensible to everyone".

To illustrate the vast scale of real-life applications of the Infinity Computer it is sufficient to mention the fields of differential equations and integration that are widely used in all kinds of software simulators of human activities, engineering calculus, scientific calculus, etc. The possibility to use in their analysis explicitly written infinitesimals and infinite numbers strongly improves accuracy of the obtained solutions and leads to completely new results in a wide range of fields spanning from fundamental physics over real-world engineering problems to social and economic sciences. The same situation holds with respect to infinity applications including such widely used mathematical tools as improper integrals, infinite series, divergent processes, infinite systems, and infinite signals.

The second group of applications can lead to completely new models and numerical toolboxes. We give just a few examples where the new computer and calculus could be applied to have a significant progress in situations unsolvable by traditional approaches: physical problems where singularities take place or situations requiring macro and micro levels of observation that usually are described by different theories that become contradictory (and, as a consequence, cannot be used) at the medium levels, i.e., at zones of their junction (e.g., gas dynamics problems, quantum and relativity approaches); mechanical engineering problems related to constructions having parts of different dimensions (in traditional approaches it is necessary to describe each of the parts separately and then to do a very complicated work joining these descriptions).

In conclusion, we advise computer scientists, mathematicians, physicists, producers of hardware, and investors to have a look at these patent and book. You will see infinite new horizons in front of you!