User blog comment:WaxPlanck/Epsilon Function/@comment-34744328-20180219194539

According to the definition, this function would only be on par with the busy beaver function, and therefore \(\epsilon(10^10)\) would in fact be comparable to \(\sigma(10^10)\), muchsmaller than Rayo's number, let alone Big foot.

If you wish to exceed the busy beaver function check out [the page] for the busy beaver function, which also describes oracle Turing machines in an easy-to-grasp manner.