Grosh and Grossuan

The Interfax agency reported on November 3, 2010 about the award of the Pythagorean award to Professor Nizhny Novgorod State University. N.I. Lobachevsky (NSU) Yaroslav Sergeev . It is noted that “the professor designed and patented a new“ computer of infinity ”” and that “he proposed a new mathematical language that allows you to record different infinitely large and infinitely small numbers.” This message needs a comment.

Sergeyev’s idea is to introduce an infinitely large number into arithmetic - Grossuan, to consider only the numbers less than this Grossuan, and to operate with them. Sergeyev arranges his idea with vague speculations, declaring the abandonment of the cantor and returning to the Greeks, formulating three of his own postulates.

The postulate 1. There are endless and endlessly small objects, but people and cars can only perform the final number of operations.

The postulate 2. What is the mathematical objects with which we work is not discussed; We only construct more powerful means that allow us to improve our capabilities to observe and describe mathematical objects.

The postulate 3. The principle formulated by the ancient Greeks is “part is less than the whole” - applies to all numbers (finite, endless and infinitely small) and to all sets and processes.

The depth of the scientificity of the postulates of Sergeev is self -evident.

Elli -Treenson, an outstanding American logician, the textbook of which has withstood many reprints and is widely used in teaching around the world, gave such a review of Sergeyev’s book “Infinity Arithmetic”, published in Italy in 2003:

The author is trying to introduce new types of numerical systems, which, according to him, have important applications. First, it views some facts about ordinary numerical systems and the theory of sets. (There is some confusion with alefs and a continuum guipothesis. For example, it defines aleph one as the number of elements of many subsets of the dominated numbers.) The systems with which it works consist of objects that are called expanded material numbers, but the descriptions of these objects and their properties are not clear enough to give any reasonable judgments about the statements that the author makes about his own about his own systems.

Sergeyev contrasts his speculations with a non -standard analysis of Abraham Robinson. Robinson Infinitezimal analysis is rightfully considered one of the most striking achievements of mathematics of the 20th century. Using subtle methods shortly before the theory of models that arose, Robinson synthesized Newton and Leibniz in the new mathematical language in early 1960. A non -standard analysis absorbed all the technical means of mathematics, based on the method of the first and last relations of Newton and on the monads of Leibniz, and explained the legitimacy of Euler's brilliant techniques using relevant infinitely large and infinitely small quantities.

Sergeev is little familiar with these scientific achievements, contrasting his good speculations to modern technologies of mathematics. However, all the linguistic and mathematical agents needed by Sergeyev have long been provided with non -standard analysis.

Sergeev will define their Grossuan as "the number of elements of the natural row." In fact, the factor of any infinitely large number is suitable for the role of this supposedly mysterious object, which are as many as you like in a non -standard analysis. This circumstance is quite obvious to specialists, but was deliberately explained in details in the Siberian Mathematical Journal, vol. 49, No. 5, 1054-1076 (2008) in order to indicate a modest place in Sergeyev’s speculation. Sergeyev’s principal gaps associated with his desire to harden the calculations with Grossian are also explained there. Unfortunately, it was not possible to stop the flow of Sergeev’s works in the variety of foreign journals in no way related to the grounds of analysis in time. True, in the mathematical database of Math-net.ru, Sergeyev does not have publications about Grossuan.

The works of Sergeyev, in the invention of new numbers and a “computer of infinity”, are poorly interesting mathematically, but very pretentious and thus unsafe speculation for science. The award of the Kroton city awards for them on behalf of the University of Calabria, where Sergeyev works, does not change the content of Sergeev’s works and his attitude to the knowledge accumulated in mathematics for the better. Grosh and Grossuan Sergeyev stand in one lexical row.

C. Kutateladze

www.mathnet.ru/php/archive.phtml?wshow=paper&jornid=smj&paperid=1902&option_lang=rus