In article <bd70785c-1e86-4437-a14e-d84028f57...@k19g2000prh.googlegroups.com>, Carl Banks <pavlovevide...@gmail.com> wrote:
> > I think people were being facetious. To me the first item in the list > is x[0]--ordinal does not match cardinal. However, I don't use > ordinals much when talking about list items; I'll say item 2, not > third item. Well, it's been said in many forms in this thread, but maybe this version will click with some. Thinking of ordinals as specifying position by order and cardinals as counting the number of steps from a specified place to an item you just have to realize that 0 and 1 based indexing have decided to use *different* definitions for the conglomerate symbols A[i] or A(i): 1 based indexing (ordinality): A[i] is the ith item in the ordered list (1st, 2nd, etc. - no need for 0th as an ordinal) 0 based indexing (cardinality): A[i] is the item i steps from the beginning of the list. I know most of what's been said is all around the above, I just thought explict statements might help. Both are prefectly reasonable and consistent definitions. Confusion only comes when you try to force the defintion of one of them on the other and then say it's illogical or not natural. Both are natural. Of course, in some languages like C an array name, say A, points to the first item in memory of the array which is assumed to be structured sequentially. Then A[0] is the first item at the address A or since we are using cardinality (0 based indexing) it's the item 0 steps from the beginning. A[1] is the item at address A+1, i.e. 1 step from the address A, the array beginning. I suspect that was a very practical choice for C since it's a systems language and down at that level you're flipping bit, bytes, addresses, etc. But a practical consequence was that there was very little +1 or -1 arithmetic necessary to manipulate the array elements. That carried over into other languages and their design. People have already pointed out the nice features of such in Python where A[n:n] is an empty list, A[:n]+A[n:]=A, etc. Now, I'm not a systems/computer guy. Just a scientist who does a lot of number crunching. But I have found out that even in that case you end of traversing lists, tuples, etc. a lot. Slicing and dicing them. And you quickly come to appreciate the 0 based approach to indexing and soon don't miss the Fortran 1-based indexing. -- -- Lou Pecora -- http://mail.python.org/mailman/listinfo/python-list
