This book introduces a disruptive computational paradigm, explaining its motivations, breakthroughs, and wide-ranging applications. For the first time, it enables numerical computations with quantities containing finite, infinite, and infinitesimal components, performed on the patented Infinity Computer. Accessible yet rigorous, the book provides a clear introduction to the paradigm and presents pioneering theoretical results, innovative numerical algorithms, efficient software implementations, and practical case studies demonstrating the transformative potential of Infinity Computing across mathematics and computer science. The author is internationally recognized for his pioneering contributions, receiving prestigious awards and delivering more than one hundred plenary lectures and tutorials worldwide. The book contains prefaces written by experts in Computer Science, Logic, Numerical Analysis, Optimization, Philosophy of Mathematics, and Set Theory. This forward-looking volume opens new horizons for researchers, engineers, professors, and students interested in next-generation supercomputing, advanced numerical methods, and the foundations of mathematics and computer science.
Reviews
"Mathematicians have never been comfortable handling infinities... But an entirely new type of mathematics looks set to by-pass the problem... Today, Yaroslav Sergeyev, a mathematician at the University of Calabria in Italy solves this problem... "
MIT Technology Review
"So, the idea that Sergeyev asks us to accept as natural is in fact a bold one, the boldest among a heap of bold proposals, but it works precisely for its boldness."
G. Lolli, Soft Computing.
The numerical nature of these new infinities and infinitesimals is one of the key differences with respect to traditional theories (Cantor, Levi-Civita, Nelson, Robinson, etc.) giving advantages in practice and opening new horizons for computer science and applied mathematics.
J. Gillard, Optimization Letters
"These ideas and future hardware prototypes may be productive in all fields of science where infinite and infinitesimal numbers (derivatives, integrals, series, fractals) are used."
A. Adamatzky, Editor-in-Chief of the International Journal of Unconventional Computing
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