Why numbering should begin 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 Original Note by Dijkstra 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 either convention two subsequences are adjacent means that the upper bound of the one equals the lower bound of the other. Valid as these observations are, they don't enable us to choose between a) and b); so let us start afresh. There is a smallest natural number. Exclusion of the lower bound —as in b) and d)— forces for a subsequence starting at the smallest natural number the lower bound as mentioned into the realm of the unnatural numbe...
