EWD831 by E.W. Dijkstra, 1982.

When dealing with a sequence of length N, the elements of which we wish to distinguish by subscript, the next vexing question is what subscript value to assign to its starting element. Adhering to convention a) yields, when starting with subscript 1, the subscript range 1 ≤ i < N+1; starting with 0, however, gives the nicer range 0 ≤ i < N. So let us let our ordinals start at zero: an element's ordinal (subscript) equals the number of elements preceding it in the sequence. And the moral of the story is that we had better regard â€”after all those centuries!â€” zero as a most natural number.

**Remark** Many programming languages have been designed without due attention to this detail. In FORTRAN subscripts always start at 1; in ALGOL 60 and in PASCAL, convention c) has been adopted; the more recent SASL has fallen back on the FORTRAN convention: a sequence in SASL is at the same time a function on the positive integers. Pity! (End of Remark.)

What's the modern trend for indexing from zero vs. indexing from one? And for specifying ranges ("from 5 to 8", `5 ≤ N < 9`

, "four elements starting from 5")? Why?

## Recent comments

2 hours 34 min ago

11 hours 57 min ago

19 hours 28 min ago

22 hours 44 min ago

2 days 3 hours ago

2 days 14 hours ago

3 days 19 hours ago

3 days 23 hours ago

3 days 23 hours ago

5 days 20 hours ago