As Guido says, 1-based indexes basically force closed ranges, so that [1, length] is the full array.
One thing that annoys me about closed ranges (and it's not much talked about) is that it is impossible to express the empty range: in python [i:i] is an empty range, while closed ranges always contain at least one element. That makes closed ranges strictly less expressive than half-open ranges, making often necessary to write special cases for zero-length.
For example when you want to split an array or a string at a given position i, the partitions will always be a[:i] and a[i:] even if one of the two is empty.
The other big issue, as many comment, is that the arithmetic to index multi-dimensional arrays is cumbersome with 1-based indexing: for example if I is a 2d image in row-major, the element (x, y) is at position I[(y - 1) * width + x] instead of I[y * width + x]. It's very easy to do off-by-one errors this way.
EDIT: adding this just to try some ASCII art :)
I think that the preference about 0-based and 1-based indexing boils down to how you reason about indexes.
I (0-indexing) think of them as the following:
|-|-|-|...|-|
^ ^
first past-the-end
position
that is, the index is
where the element begins. This way there is a special endpoint, the "past-the-end", where the an appended element would begin. In particular, an empty array has both first and last endpoint equal to 0.
I believe that people who favor 1-based indexing think like this
|-|-|-|...|-|
^ ^
first last
element element
that is, in the
ordinal way, i is the i-th element.
One thing that annoys me about closed ranges (and it's not much talked about) is that it is impossible to express the empty range: in python [i:i] is an empty range, while closed ranges always contain at least one element. That makes closed ranges strictly less expressive than half-open ranges, making often necessary to write special cases for zero-length.
For example when you want to split an array or a string at a given position i, the partitions will always be a[:i] and a[i:] even if one of the two is empty.
The other big issue, as many comment, is that the arithmetic to index multi-dimensional arrays is cumbersome with 1-based indexing: for example if I is a 2d image in row-major, the element (x, y) is at position I[(y - 1) * width + x] instead of I[y * width + x]. It's very easy to do off-by-one errors this way.
EDIT: adding this just to try some ASCII art :)
I think that the preference about 0-based and 1-based indexing boils down to how you reason about indexes.
I (0-indexing) think of them as the following:
that is, the index is where the element begins. This way there is a special endpoint, the "past-the-end", where the an appended element would begin. In particular, an empty array has both first and last endpoint equal to 0.I believe that people who favor 1-based indexing think like this
that is, in the ordinal way, i is the i-th element.