The Mathematical Intelligencer 37 (2):4-8 (2015)

Yaroslav Sergeyev
Università della Calabria
Several ways used to rank countries with respect to medals won during Olympic Games are discussed. In particular, it is shown that the unofficial rank used by the Olympic Committee is the only rank that does not allow one to use a numerical counter for ranking – this rank uses the lexicographic ordering to rank countries: one gold medal is more precious than any number of silver medals and one silver medal is more precious than any number of bronze medals. How can we quantify what do these words, more precious, mean? Can we introduce a counter that for any possible number of medals would allow us to compute a numerical rank of a country using the number of gold, silver, and bronze medals in such a way that the higher resulting number would put the country in the higher position in the rank? Here we show that it is impossible to solve this problem using the positional numeral system with any finite base. Then we demonstrate that this problem can be easily solved by applying numerical computations with recently developed actual infinite numbers. These computations can be done on a new kind of a computer – the recently patented Infinity Computer. Its working software prototype is described briefly and examples of computations are given. It is shown that the new way of counting can be used in all situations where the lexicographic ordering is required.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

 PhilArchive page | Other versions
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

Add more citations

Similar books and articles

Flags, Medals, and Decorations.Gustavo Tracchia - 2007 - Raven: A Journal of Vexillology 14:85-104.
The Exact (Up to Infinitesimals) Infinite Perimeter of the Koch Snowflake and its Finite Area.Yaroslav Sergeyev - 2016 - Communications in Nonlinear Science and Numerical Simulation 31 (1-3):21–29.
Lagrange Lecture: Methodology of Numerical Computations with Infinities and Infinitesimals.Yaroslav Sergeyev - 2010 - Rendiconti Del Seminario Matematico dell'Università E Del Politecnico di Torino 68 (2):95–113.
Reverse Mathematics and Rank Functions for Directed Graphs.Jeffry L. Hirst - 2000 - Archive for Mathematical Logic 39 (8):569-579.
Caracterización en lenguajes lógicos infinitarios de los órdenes parciales diseminados contables.Begoña Carrascal - 1994 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 9 (1):173-184.
Complexity Ranks of Countable Models.Su Gao - 2007 - Notre Dame Journal of Formal Logic 48 (1):33-48.
Rank, Join, and Cantor Singletons.Jim Owings - 1997 - Archive for Mathematical Logic 36 (4-5):313-320.


Added to PP index

Total views
87 ( #107,811 of 2,340,044 )

Recent downloads (6 months)
18 ( #36,049 of 2,340,044 )

How can I increase my downloads?


My notes