This is an exercise in critical thinking. I am not looking, therefore, for opinions on the matter; rather: I would like to know the evidence (whatever that might mean). Background: I have a longstanding interest in different types of logic: The Adjunction $\_\times A\dashv (\_ )^A$ for Preorders...

By defining $$ f_n(x) = \int_{0}^{x}\int_{0}^{x_n}\ldots\int_{0}^{x_2}e^{\frac{1}{\log x_1}}\,dx_1\,dx_2\cdots dx_n $$ we have $$ f_n(x) = \int_{0<x_1 < x_2<\ldots<x_n<x}e^{\frac{1}{\log x_1}}\prod dx_k = \int_{0}^{x}\,\frac{1}{(n-1)!}(x-x_1)^{n-1}e^{\frac{1}{\log x_1}}dx_1$$ and by letting $x_1 ...