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After works of Davis, Matijasevic, Putman and Robinson between 1960 and 1970, we know that every recursively enumerable set of numbers can be represented by a polynomial. In particular, it's the case ...

There is simple equation $x^y=y^x$. By taking logarithm we can see that it is equivalent to $\frac{\ln x}{x}=\frac{\ln y}{y}$. When we plot and inspect the function $f(x)=\frac{\ln x}{x}$, we can see ...