I have read the article (in Polish): Jozef H. Przytycki, “Grigorij Perelman, Poincare’s hypothesis and rejected Fields’ Medal”, Wiadomosci Matematyczne (Annales Societatis Mathematicae Polonae Series II), vol. 46, No. 1, 37 – 61 (2010), where among others, there has been written that Prof. Perelman has said that Fields’ Medal has not been of interest for him and everyone has understood that if the proof is correct, then no other form of applauding is necessary.

Well, the authors of the paper: T. J. Stępień, Ł. T. Stępień, „On the Consistency of the Arithmetic System”, Journal of Mathematics and System Science, vol. 7, 43 (2017), arXiv:1803.11072, have not any problems with an excess of fame. The proof of the consistency of the Arithmetic System published there and done within this system, is correct, and this apparently must be sufficient for them…

]]>Let’s suppose Alice and Bob do not use 100 $, but 10 $, and not an n=51% head biased coin, but an n=99.99% head biased coin – (I thought) end of story.

Then, I had a friend pointing out that (surprisingly) the statement “[..] both eventually go broke [..]” gives no reason to assume convergence of average k~ (=number of tosses) for Alice and/or Bob to become broke; moreover, k~ depends on n=bias and on the initial number of dollars, and it is (obviously) different for Bob and for Alice; so it is not (necessarily) the same problem.

I feel the answer stays the same; but now, the prove of the same distribution by having constant ratio does not appear to be rigorous enough…

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