Why numbering should start at zero To denote the subsequence of natural numbers 2, 3, ..., 12 without the pernicious three dots, four conventions are open to us a) 2 ≤ i < 13 b) 1 < i ≤ 12 c) 2 ≤ i ≤ 12 d) 1 < i < 13 Are there reasons to prefer one convention to the other? Yes, there are. The observation that conventions a) and b) have the advantage that the difference between the bounds as mentioned equals the length of the subsequence is valid. So is the observation that, as a consequence, in ...