> 1:6 which is more natural than 0:5 (from the 0th to the 5th)
This is again just begging the question. When you want to refer to the initial element as the "1st", it is due to the established convention of starting to count from 1. The point is that the reasonining for starting from 1 might only be that: conventional, not based on some inherent logic.
You start counting with 1 because 0 is the term created later to indicate an absence of stuff to count. If I have one kid, I start counting by the number one, if I have 0 kids I don't have anything to count.
But then I agree that there is no inherent logic, math is invented and not discovered, and you could define it any way you want. If we all had 8 fingers we would probably use base 8 instead of 10 after all.
Actually we naturally count from 0, because that's the initial value of the counter.
It just so happens that this edge case of 0 things doesn't occur when we actually need to count something. Starting from 1 is kinda like head is a partial function (bad!) in some functional programming languages. Practicality beats purity.
This is again just begging the question. When you want to refer to the initial element as the "1st", it is due to the established convention of starting to count from 1. The point is that the reasonining for starting from 1 might only be that: conventional, not based on some inherent logic.