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There has been controversy about Sergeyev’s work and its applications. It is the contention of the reviewer that the Sergeyev grossone, , can simply be interpreted as a generic large natural number and that there is no new theory of infinity involved. Part of the controversy stems from the fact that Sergeyev does not make an attempt to give a logical foundation for his new idealized infinite and infinitesimal elements. For example, we can write

Numerical infinities and infinitesimals: Methodology, applications, and repercussions on two Hilbert problems