Georg Cantor published his theorem in 1891 that the powerset of a set has higher cardinality than the set itself, which theorem transformed the mathematics.
Cantor launch the foundations of mathematics through the set theory with this theorem, and has not been able to halt this trend the running aground of naive set theory. The Cantor's naive set theory later replaced by a bunch of different axiomatic theories, which only top-level professional mathematical training of students learned detail. But all axiomatic theories implicitly or explicitly organically built on Cantor's theorem, and his naive approach on set theory.
Now 121 years to Cantor's theorem published, and certainly no wonder that if I declare and prove that Cantor's theorem is incorrect, then this acceptance and understanding encounters a very high resistance. Although Cantor's theorem untenable it became apparent to me in February of 2001 on an Internet forum for discussion, but I not surprised still now that this communication so difficult. If the question is simple would, then not have been 121 years apart, to reveal of the here discussed problems. So do not expect anyone to very easily understandable relationships, in any event, to my understanding there is no need for special high-level mathematics qualification, so anyone who is interested in mathematics, can meet here interesting issues.
Although I would have liked when my writing appears in a hungarian mathematical journal, not in my own blog, but the editor's view my writing has no scientific value, and is full of inaccuracies. And although the editor's expertise does no doubt, but in our correspondence after seven exchange of letters could not write any refutation of my statements, of course, so he could not convince me, even actually, he not really tried this. It is true also that the claim that the increasing infinite cardinalities form an infinite series also, lost the only theoretical support is also with refutation of Cantor's theorem, and so mathematical disciplines on based on this, which specializing in the editor's also need of full reconstruction.
In contrast, some of our correspondence was discussed interesting topic also regarding the nature of mathematics, which in our the points of view significantly different from also, so I will be sorted this part of our correspondence in below. Even more so, because the editor's position was not an isolated opinion, but I think from the earlier discussions of the Internet, predominantly characterize in the current formal perception of mathematics. In my view, this erroneous assessment of the theoretical foundations of the mathematics seriously crippling the mathematical thinking.
Maybe a few years ago I have not blogging, but also I try door handle at other mathematical journal, but in the meantime so much changed the operation of the intellectual world in thanks the global prevalence of the internet that I choose this new, simpler, and perhaps more efficient way to distribute my thoughts.
First of all, you can view the original article in Hungarian (A Cantor tétel cáfolata) and version of English (The refutation of Cantor's theorem), which I began to formulate the autumn of 2011 and were completed in May. The writing has slowed for the English language quite weak relationship with me, so I followed the path of the text-simplification that what I was able to be drafted in English, I wrote it in Hungarian as well. Be noted that example of the endless ladder is idea of an earlier debate partner, Zoltan Bodi (ksh.hu). The criticism of the most common objections to made in relation to the article I deal separately (serial number of subset of even numbers). I write a very surprising consequence separately (set of rational numbers is the set of real numbers). Readable the English version (The set of rational numbers equal with set of real numbers).
Just in my last letter to editor I realized new arguments connection the refutation of Cantor's theorem, so the last chapter second paragraph I would do writing now otherwise, as the new argument is due to become obsolete, but I detail rather elsewhere (Russell, Cantor analogy).
But the most interesting, and most interest for the public my opinion about the mathematics, which are summarized in my last letter for the editor (What is the mathematics). Of course, the editor's views and opinions will not tell you in this letter, but not my goal is this topic, which is exactly the goal, I confer with that appreciation about the mathematics, and theoretical foundations. Because the text taken from an e-mail, a vertical line at beginning of a line is a quotation, and two vertical lines at the beginning of a line is a quotation inside a quotation.
From previously described can be drawn the conclusion that the Russell paradox is not fiasco of set theory, but in is an isolated contradictory logic example, and that this paradox with faulty Cantor's item is needless astray drove to the development of mathematics, even if, nevertheless, and in spite of these errors was able to many achievements.
In addition, you must also be concluded that the concept of the series is not compatible with the concept of the set, and all such attempts inevitably born a contradiction. Although no theoretical obstacle to the series is treated as a set, but that's a different and unexpected places avenge himself. A series of elementary allegations based on induction contrary to the allegations based on set theory, but instead of we draw from this the necessary conclusions, we abuse our logical thinking and excuses we produce, how could stick to at a heterodoxy.
This blog is a plan to start a constructive mathematics discussion. Because I do not have any meaningful criticism or acclaim so I hope one of them it will happen soon. Therefore, any meaningful comment I expect and welcome. Because I want preserve the talk quality, so I leave only those postings, wich free from personal remarks, insults and really meaningful, so either contain real mathematical ideas in the arguments or otherwise significantly related with thoughts in article. Possible to send private message to takacs.ferenc.bp@freemail.hu address (I speak only Hungarian).
About me just say to in 1981, I graduated from ELTE Department of programmer mathematician, and since then I write computer programs. Before this 1975, I won a national mathematics competition for apprentices and this is for me surprising sequel directed my attention towards mathematics.
Since only a few articles I translated into English, so other thoughts unfortunately only available in Hungarian. I hope this will change in the future but have not yet done much in this direction.
Because I can only draw attention to my thoughts in a small group, so I would like to ask my readers that if they find my articles interesting then recommend this blog to acquaintances also, otherwise it existence stays a secret as before the birth of it. Share or refute! You do not want to conceal as an outsider?
