Umm, no? Indices are ordinals[0], forming the canonical/nominal well-ordering of a collection such as a array.
> an ordinal number, or ordinal, is one generalization of the concept of a natural number that is used to describe a way to arrange a (possibly infinite) collection of objects in order, one after another. [...] Ordinal numbers are thus the "labels" needed to arrange collections of objects in order.
In C an object can be larger than PTRDIFF_MAX, a real possibility in modern 32-bit environments. (Some libc's have been modified to fail malloc invocations that large, but mmap can suffice.) Because pointer subtraction is represented as ptrdiff_t, the expression &a[n] - a could produce undefined behavior where n is > PTRDIFF_MAX. But a + n is well defined behavior for all positive n (signed or unsigned) as long as the size of a is >= n.
There's an asymmetry between pointer-pointer arithmetic and pointer-integer arithmetic; they behave differently and have different semantics. Pointers are a powerful concept, but like most powerful concepts the abstraction can leak and produce aberrations. I realize opinions vary on whether to prefer signed vs unsigned indices and object sizes (IME, the camps tend to split into C vs C++ programers), but the choice shouldn't be predicated on the semantics of C pointers because those semantics alone don't favor one over the other.
