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I feel like this is more of a programming techniques question than anything else, since the issues is about data type conversion. So you want to convert from float to int. So here is my suggested code (this should work. If not, tell me and I will edit this): // Hyperoperation type 4: public double tetrate(double a, double b) { double total = a; int ...


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Lars Kindermann in his dissertation discusses fractional iteration with the following focus: Consider the production of sheets of steel in a sequence of similar machines (pressing and bowing that sheets to bring it into form), say, seven such machines behind each other. Then you can measure the sheets before the first and after the last, but you cannot (by ...


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I was looking for the more general case where we find the continuum between the operators themselves - add, multiply, and exponentiation or even higher. I think that this is stictly related to the extension of the Ackermann Function to non-integer values: I guess we can call the problem "non-integer ranks problem" because it has to do with ...


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There is (at least) one option - however depending on whether a solution for the problem of "fractional iteration of logarithm" is available (aka: "Tetration". Note that in the tetration-forum there is an exchange on various approaches to this problem). Assume for the moment that a version of that fractional iteration is available, and let us ...


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Actually you fixed $x$ and you're trying to find the limit so in the first case, if $k$ is the limit then $\sqrt[k]k=x$ and in the second case if $k$ is the limit then $x=e^{\frac{W(k\ln(k))}{k}}$ ( you made a mistake) but actually the two equations are equivalents : $$x=\sqrt[k]k\iff x=e^{\frac{\ln(k)}{k}}\iff x=e^{\frac{W(k\ln(k))}{k}}$$ using the fact ...



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