I should be very close to the final mathematical proof now. I still have to grasp the results and try to prove it. In any case, I have my zero element that transfers a number into itself when added. And the one-element that does the same for multiplication. With my triple tuple, it's easy (0, 0, 0) and (1, 1, 1). Calculating this in old figures is a considerable surprise. The numbers, and thus the universe, are periodic.
(0, 0, 0) = 0 * 0 + 1 * 0 + infinity * 0 = -1 + epsilon + 0(infinity).
This results in infinity times zero + 1 * 0 = 1. This results in the above the old 0.
(1, 1, 1) is then the hammer. 1 * 0 + 1 * 1 + infinity. To map this to 1, infinity + epsilon must be the old 0.
The proof will be exciting. If you don't understand anything now, you should read in my wiki: Division by zero