If Nothing Was Impossible
What if we’re wrong and zero isn’t really a viable number? That’d rule out the whole decimal system. No more places of tens. Every number would be either a fraction or an integer. Integers would start at 1 and never become more than one column wide. Just a big infinite stack of single digits representing ever number imaginable; each one a unique symbol somehow. Base ten, meet base eternity. The square root of two would be an imaginary number. Subtracting 2 from 2 would be like dividing by zero.
If you stop using math as an abstraction and link it to physical phenomena like the Babylonians and Egyptians used to, it’s hard to imagine zero. There’s always something. And even if there isn’t, lack of something isn’t exactly a quantity. Zero is an antiquantity. Is that enough to make it a number? That’s like saying waste, which is the antiproperty, is actually a form of property. But that’s ridiculous: I have to want to own property to exhibit ownership, and waste is waste specifically because I don’t want to own it.
If I knew my ‘rithmetic I’d write up a proof, but for now this is just a nonzero brain fart. Thank you for indulging me.