Question

Mathematicians typically count starting with 1, and call the counting variable n (i.e. “the nth term of the sequence). Computer scientists typically count starting with 0, and call the counting variable i (i.e. “the ith index of the array”). Which is why I was confused to learn that Seq.nth actually returns the “n+1 term of the sequence”.

Doubly confusing is that Seq.iteri does as it’s name implies and traverses a sequence supplying the current index.

Am I missing something? Is there a rational / history for this misnomer / inconsistency? Or was it just a mistake (which likely can’t be fixed since we have a commercial release now).

Edit

Admittedly my claim about conventional use of i and n is not strictly true and I should have been more careful about such an assertion. But I think it is hard to deny that the most popularly used languages do start counting at 0 and that i and j are most certainly extremely popular choices for index variable names. So, when I am familiar with using Seq.iteri and Seq.mapi and then come across Seq.nth I think it is reasonable to think, “Oh, this function counts differently, probably the other way things are counted, starting with 1.”

And, as I pointed out in the comments, the summaries for Seq.iteri, Seq.mapi, and Seq.nth only served to enforce my assumption (note that intellisense only gives you the summaries, it does not give you the description of each parameter which you have to find on MSDN):

Seq.iter

Applies the given function to each
element of the collection. The integer
passed to the function indicates the
index of element.

Seq.mapi

Creates a new collection whose
elements are the results of applying
the given function to each of the
elements of the collection. The
integer index passed to the function
indicates the index (from 0) of
element being transformed.

Seq.nth

Computes the nth element in the
collection.

Note the emphasis on “nth”, not mine, as if everyone knows what the nth element in the sequences is as opposed to the ith element.

Answer 1

Talking of history, nth is zero based in Lisp, which is probably what the F# function is named for. See the common lisp spec for nth.

I haven’t found your statement about i and n in mathematics to be true; usually n is the number of something rather than an index. In this case, it was the number of times to call cdr to get the next element.