Indeed Immanuel or Laplaces Demon, which rules out the chances of God being able to be omniscient because of the infinite memory rquirements exceeding the amount of information that could be known, by ironically saying the opposite.
It must be admitted that the openness of the future would be hard to defend in the rigidly deterministic universe that Laplace regarded as the inexorable consequence of taking Newtonian ideas seriously. We have seen that in that world, full knowledge of the present, together with unlimited calculating power, implies total knowledge of a rigorously entailed past and future. Nothing really novel ever happened; history was a reiterated tautology. However, the iron grip of Laplace's calculating demon has been relaxed by the twentieth century discovery of widespread intrinsic unpredictabilities present in nature, both at the microscopic level of quantum events and also at the macroscopic level of the behavior of exquisitely sensitive chaotic systems. We have noted already that the question of whether these epistemological deficiencies are to be interpreted as signs of an ontological openness is a metaphysical issue, not to be settled by the natural sciences alone. In the case of chaotic systems, we have seen that it is possible to develop an interpretation that leads to the existence of extra causal principles with the form of the 'active information', and that these might well be capable of accommodating the action of both human and divine agency. Such a program would then achieve Pannenberg's desired defense of the openness of history, as theology wishes to understand it, not by appeal to field theory but to the ideas of the top-down effects of active information. There is much that is necessarily speculative here, but I believe that these ideas afford a better model than field for the presence and activity of the Spirit.[10]
—John Polkinghorne, Faith, Science and Understanding
There's only one infinity you can use or manipulate in any reliable way, the universe which is infinite but finite in size. It is the set of existence to which as far as we know or indeed can most likely ever know, everything belongs, there are no null sets. It is also expanding probably as fast if not faster than the speed of light so it is also unbounded too. It is what the ancient Greeks would of called a countable infinity, as opposed to an uncountable one.