## Books

## Yaroslav D. Sergeyev, *Arithmetic of Infinity*

**Paperback edition is available at European Amazon sites:**** UK****,**** DE****,**** FR****,**** IT****,**** ES****Revised electronic edition is available at Amazon sites:**** ****COM****,**** UK****,**** DE****,**** FR****,**** IT****,**** ES****,**** CA****,**** JP****,**** BR****,**** IN****,****MX**

**1****2.02.2016 Amazon.it Kindle Store Best Sellers Rank:****# 1 in eBook Kindle > eBook in lingua straniera > eBook in inglese > Scienze, tecnologia e medicina > Matematica**

The book presents a new methodology that allows one to represent infinite and infinitesimal numbers by a finite number of symbols and to execute arithmetical operations with all of them in the same manner as we are used to do with finite quantities. The new approach is not related to the non-standard analysis and infinity is considered in the book in a coherent way different from those proposed by Georg Cantor, Abraham Robinson, and John Conway. However, the new approach does not contradict Cantor, it evolves his theory and supplies new more powerful tools to deal with different infinite and infinitesimal quantities.

From the methodological point of view, the principle of Ancient Greeks ‘The part is less than the whole’ is adopted and applied to all quantities (finite, infinite, and infinitesimal) and to all sets and processes (finite and infinite). The new positional system with the infinite radix introduced in the book allows one to consider infinite, finite, and infinitesimal numbers as particular cases of a unique framework. The new viewpoint gives detailed answers to many questions and paradoxes regarding infinite and infinitesimal quantities. Particularly, applications of the new approach to limit theory, measure theory, and set theory are given.

The book is mainly addressed to mathematicians, computer scientists, philosophers, physicists, and students. However, it is written in a popular way in order to allow any person having a high school education and interests in the foundations of these sciences to understand it easily.

From the methodological point of view, the principle of Ancient Greeks ‘The part is less than the whole’ is adopted and applied to all quantities (finite, infinite, and infinitesimal) and to all sets and processes (finite and infinite). The new positional system with the infinite radix introduced in the book allows one to consider infinite, finite, and infinitesimal numbers as particular cases of a unique framework. The new viewpoint gives detailed answers to many questions and paradoxes regarding infinite and infinitesimal quantities. Particularly, applications of the new approach to limit theory, measure theory, and set theory are given.

The book is mainly addressed to mathematicians, computer scientists, philosophers, physicists, and students. However, it is written in a popular way in order to allow any person having a high school education and interests in the foundations of these sciences to understand it easily.

**13.06.2014 Amazon.com Best Sellers Rank:**

#1 in Books > Science & Math > Mathematics > Infinity

#1 in Kindle Store > Kindle eBooks > Nonfiction > Science > Mathematics > Infinity

#1 in Books > Science & Math > Mathematics > Infinity

#1 in Kindle Store > Kindle eBooks > Nonfiction > Science > Mathematics > Infinity