An ordered collection of things starts no things from the beginning. A journey starts 0 metres from the origin. If you count the number of _ you are along you

An ordered collection of things starts no things from the beginning. A journey starts 0 metres from the origin. If you count the number of _ you are along your journey and start with 1, then at the second metre you are at the 101st centimetre. When someone says how many dragons have you slain? Just as you leave and haven't heard of any dragons yet, you don't say "I'm slaying my first dragon now" Every construction of the natural numbers I have seen starts with 0. The first hour of the day has passed when the clock strikes one. The hour preceding that is the same day. English calls it 12 because it was invented before we had a firm grasp of zero and english is inconsistent. 24 hour clocks call it 00. 1 based indexing can be correct, but 1 based ordered discrete sets map incredibly poorly to any ordered set with a different number of elements (such as the reals). Additionally dealing with ranges is less easy to make consistent. 0 based indexing is always correct.