[jacknews]

'associated'? Sounds nice, but not very convincing, except perhaps the zeroth item of an ordered set should be just that, 0.

I agree indexing is a trade-off, sometimes 0 is best, sometimes 1 makes more sense.

But it's not linguistic 'similarity'. You have to name things. If your names are off-by-one (the element named 'first' is actually the second) you're just sowing confusion.

[afiori]

sometime ordinals are more natural sometimes cardinals are more natural.

In the case of vectors (especially of C-style arrays) I would say that A[0] is the first element in the array. I agree that things should have names, but names serve us, not us them.