Raphael R.
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 Aug9 comment square root of complex number in a resolvent operator I understand what you are saying, but I find it strange that to get the final result you have to perform the modular reduction to obtain $\sqrt{-(\lambda +i\epsilon)}$ for one of the $\sqrt{-\lambda}$ (the one in the denominator), and for the other (in the exponential of $R_{\lambda}$) you cannot use it. Moreover, that the sign $|x-y|/{2\sqrt{\lambda}}$ is dependent on these things is another concern to me. May5 comment Unusual Application of Stokes Theorem Yes, and it is still unclear to me how the commutator comes from the double integral... Mar25 comment Real numbers as n-ary fractions Thanks. It all makes sense now. Mar22 comment How to show Dedekind's definition of an irrational number is equivalent to Cantor's definition? Ok. That's an elegant proof. Thank you. However, it does not use the lemma given in the problem, and I am very curious as how that lemma would be used to show this relationship between Dedekind cuts and Cauchy sequences, since I am not happy with the way I tried to use the lemma to solve this. Mar22 comment How to show Dedekind's definition of an irrational number is equivalent to Cantor's definition? I am not so sure about that. The problem I am trying to solve gives a hint that was not employed in any of the cited discussions, and it might turn to be a different proof, which could be very interesting.