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.
|Number of pages||17|
|Journal||Foundations of Science|
|State||Published - 1 Sep 2017|
Bibliographical noteFunding 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.
© 2016, Springer Science+Business Media Dordrecht.