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A few days ago I had a crazy idea that counting numbers (first, second, etc) should start with zeroth instead of first. Not only would that help with teaching programming, but also many real world confusions and off-by-one errors would go away. Compare this:
to this:
Of course that would never happen, but as a thought experiment, I rest my case :-)
An interesting demonstration of the arbitrariness of ordinal numbers is that Romans didn't count like we do. They counted sheep like us, but they counted days differently. Our modern calendar goes from the year -1 to the year +1 and you seem to propose going from -0 to +0. But the Roman calendar went from the day -2 to the day +1. Similarly, when the Greeks told them to put in a leap day "every fourth year" they put one in every third year.