I'm creating a world in which definitions are consistent as much as possible
Before you complain again that remembering how "base d is defined by 0 -> d-1 numbers" consider that in decimal 0 -> 9 is ten numbers. The pattern is true for all bases. In your system, instead of having a true decimal system of ten numbers, we have nine. WTF?
Math happens to be one of the most consistant things around. If you want to define something mathematically, you submit a proof that your calculations are correct, and ideally it is consistant with what was true before. Math very rarely is supposed to relate to anything in the physical world anymore. That's why I told you to go back to Babylon, where you will happily find that there is no way to express "nothing-ness" in a rigourous sense.