Author of What is Number?
disclaimer: I have no intention of furthering this incomplete work. Completion of the work will likely either occur through the development of powers of one in the context of equivalence classes, which will demand also intuition, else use for closing the case on division by zero. To any who intend to develop further the section of probabilities on infinite quantities, a word of caution. Further inspection has led to the realization that the interpretation I have provided is lacking at best, otherwise incorrect. You will see this result by taking powers of two at even positions relative to the set of all powers of two, and find that it is not 1/2 as it should be. Perhaps this is correctable with some form of "regularization".
Jordan Lee Hess