Why numbering should start at zero

In Python, range() defines all integers in a half-open interval. So range(2, 10) means, speaking mathematically, [2, 10). Or, speaking Python, [2, 3, 4, 5, 6, 7, 8, 9].

Despite asymmetry, that is not a mistake nor an accident. It makes perfect sense since it allows you to glue together two adjacent intervals without risk of one-off errors:

[a, c) = [a, b) + [b, c)

Compare to closed intervals that feel more “natural”:

[a, c] = [a, b] + [b+1, c]

This is also a reason for indexing to start from zero: range(0, N) has exactly N elements.

Dijkstra wrote an excellent article on the subject back in 1982.