Grossone Infinity Computing

  • Yaroslav D. SergeyevEmail author
Reference work entry
Part of the Encyclopedia of Complexity and Systems Science Series book series (ECSSS)


Extended natural numbers

Positive integers larger than grossone.


The number of elements of the set of natural numbers expressed by the symbol ①. It allows to represent this set as {1,2,3,…① − 2,① − 1,①}.

Infinity computer

A new supercomputer patented in USA, Europe, and Russia allowing one to work numerically within finite, infinite, and infinitesimal numbers.

Infinity computing

Numerical computations on the Infinity Computer using the principle “The part is less than the whole” applied to all numbers (finite, infinite, and infinitesimal) expressed in the positional numeral system with the base ①.

Numbers and numerals

A numeral is a symbol (or a group of symbols) that represents a number. A number is a concept that a numeral expresses.


A tribe living in Amazonia nowadays. These people use an extremely simple numeral system for counting: one, two, and many. For Pirahã, all quantities larger than two are just “many” and such operations as 2 + 2 and 2+1 give the...


Numbers and numerals Grossone-based numerals Numerical infinities and infinitesimals Infinite sets 


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University of CalabriaRendeItaly
  2. 2.Lobachevsky State UniversityNizhni NovgorodRussia
  3. 3.Institute of High Performance Computing and NetworkingC.N.RRomeItaly

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