  After generalizing the Archimedean property of real numbers in such a way as
to make it adaptable to non-numeric structures, we demonstrate that the real
numbers cannot be used to accurately measure non-Archimedean structures. We
argue that, since an agent with Artificial General Intelligence (AGI) should
have no problem engaging in tasks that inherently involve non-Archimedean
rewards, and since traditional reinforcement learning rewards are real numbers,
therefore traditional reinforcement learning probably will not lead to AGI. We
indicate two possible ways traditional reinforcement learning could be altered
to remove this roadblock.
