Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
The Mathematical Intelligencer Flunks the Olympics. / Gutman, Alexander E.; Katz, Mikhail G.; Kudryk, Taras S. и др.
в: Foundations of Science, Том 22, № 3, 01.09.2017, стр. 539-555.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - The Mathematical Intelligencer Flunks the Olympics
AU - Gutman, Alexander E.
AU - Katz, Mikhail G.
AU - Kudryk, Taras S.
AU - Kutateladze, Semen S.
N1 - Funding Information: We are grateful to Rob Ely for helpful suggestions. We thank the anonymous referee for Foundations of Science for helpful comments. M. Katz was partially funded by the Israel Science Foundation Grant No. 1517/12. Publisher Copyright: © 2016, Springer Science+Business Media Dordrecht..
PY - 2017/9/1
Y1 - 2017/9/1
N2 - The Mathematical Intelligencer recently published a note by Y. Sergeyev that challenges both mathematics and intelligence. We examine Sergeyev’s claims concerning his purported Infinity computer. We compare his grossone system with the classical Levi-Civita fields and with the hyperreal framework of A. Robinson, and analyze the related algorithmic issues inevitably arising in any genuine computer implementation. We show that Sergeyev’s grossone system is unnecessary and vague, and that whatever consistent subsystem could be salvaged is subsumed entirely within a stronger and clearer system (IST). Lou Kauffman, who published an article on a grossone, places it squarely outside the historical panorama of ideas dealing with infinity and infinitesimals.
AB - The Mathematical Intelligencer recently published a note by Y. Sergeyev that challenges both mathematics and intelligence. We examine Sergeyev’s claims concerning his purported Infinity computer. We compare his grossone system with the classical Levi-Civita fields and with the hyperreal framework of A. Robinson, and analyze the related algorithmic issues inevitably arising in any genuine computer implementation. We show that Sergeyev’s grossone system is unnecessary and vague, and that whatever consistent subsystem could be salvaged is subsumed entirely within a stronger and clearer system (IST). Lou Kauffman, who published an article on a grossone, places it squarely outside the historical panorama of ideas dealing with infinity and infinitesimals.
UR - http://www.scopus.com/inward/record.url?scp=84961145161&partnerID=8YFLogxK
U2 - 10.1007/s10699-016-9485-8
DO - 10.1007/s10699-016-9485-8
M3 - Article
AN - SCOPUS:84961145161
VL - 22
SP - 539
EP - 555
JO - Foundations of Science
JF - Foundations of Science
SN - 1233-1821
IS - 3
ER -
ID: 9048930