Huh. This is not my field, so I am hesitant to comment in detail. However, a few things quickly strike me as troubling about the original paper: * The work is

Huh. This is not my field, so I am hesitant to comment in detail. However, a few things quickly strike me as troubling about the original paper: * The work is based on "a new applied point of view on infinite and infinitesimal numbers", the cited source of which is six papers by the same author as the current one. Apparently, nobody else has chosen to work on it. * The postulates behind this method include the statement that "We shall not tell what are the mathematical objects we deal with", and because of this, "such concepts as bijection, numerable and continuum sets, cardinal and ordinal numbers cannot be used in this paper". In other words, the author is knowingly setting aside most of what I consider to be the essential features of mathematics. * I have serious doubts that results or concepts that boil down to "infinity minus three" or "infinity times 8/9" would prove to be robust if you considered different infinite sequences with the same limit. I haven't looked up the author's other papers on the subject, but I don't see any evidence that he has addressed this issue. * This paper (and several of the earlier ones) was apparently published in the journal "Chaos, Solitons, & Fractals" in a 2009 volume. You may recognize that title from recent discussions of Elsevier: a scandal unfolded in 2008-9 where the journal's editor, El Naschie, was found to have published hundreds of his own papers (whose merit has been questioned) and accused of poor editorial standards.[1] It may or may not be meaningful that the current paper's first four references are all to El Naschie's work. In short, my impression is that this paper is based on decidedly non-mainstream mathematics, and I see no reason to be excited about its claims or conclusions. [1] http://en.wikipedia.org/wiki/Elsevier#Chaos.2C_Solitons_.26_Fractals http://en.wikipedia.org/wiki/Elsevier#Chaos.2C_Solitons_.26_... http://backreaction.blogspot.com/2008/11/chaos-solitons-and-self-promotion.html http://backreaction.blogspot.com/2008/11/chaos-solitons-and-... http://elnaschiewatch.blogspot.com/2009/02/that-hard-to-find-baez-material.html http://elnaschiewatch.blogspot.com/2009/02/that-hard-to-find... (The archived posts by Baez here are the point; I know nothing about this site itself.)