>>13496286>Where your cognitive dissonance is popping in is ignoring the fact that the hypothesis is about the Riemann-zeta function is defined in terms of infinite sets and depends on the undefined notion of an "infinite set" whatever that means and the ill-defined notions of set theoryThere are many classically equivalent formulations of the question, one of them being the assertion that a certain algorithm doesn't halt. The problem stated in such a way does in involve any set theory or notions of infinite sets.
>You don't have anything that lets you run infinite algorithms.You misunderstand. The algorithm is very finite. It's just like any other kind of program you run on your computer. A finite amount of code that you can execute.
The empirical meaning of the Riemann Hypothesis is then that no matter for how long you execute the algorithm, you will never reach the halt state. It's completely imaginable that in process of actually executing it, you would reach the halt state, and the RH asserts that this would never happen. Thus RH restated in such a way has clear empirical meaning.
>This idea of "convergence" is a nice little guess carried over from applications, but it doesn't really mean anything logicallyThere are no sets, no convergence, just purely finite stuff involved. Finite computations on finite resources, with clear and unambiguous meaning.
