>and they had a name for whatever was before 1

What they have merely names what Americans name as zero.

But it's not a stand-in for zero, for us, it's a different entity (a different thing).

A floor (etage, piano, orofos, etc) is a "layer of building where people live above the ground level layer".

So there's no zero-based indexing of floors, because the first item in the set of what are considered as floors is called "first" (e.g. primo in italian).

So, the thing one must understand before they say "same difference", is the other cultural difference: that most European countries don't consider the ground level "floor" to be a floor/story.

I.e, we don't consider the upper floors and the "ground floor" to be in the same set. Which is also why we don't count them when we say a "2 story house" (and we mean a house with 3 such layers, ground story + 2 stories).

Is there a zero-based indexing of the whole "heterogenous" set of ground level + floors?

Well, it's common to have the ground level designated with G or national specific names: BG, BV, E, IS, PB, PT, RC, S, P, PK, etc.

It's just that in some elevators 0 is a substitute for this -- which is probably due to the few common brands and parts being international and nobody bothering to change them (e.g. Otis). That's more a red herring than how Europeans think about floors or index them.

>> So there's no zero-based indexing of floors, because the first item in the set of what are considered as floors is called "first" (e.g. primo in italian).

So the floors are numbered according to their distance above the ground level (whatever that's called). This matches my suggestion of treating zero-based indexing as a distance from the first element.

>> Is there a zero-based indexing of the whole "heterogenous" set of ground level + floors?

Yes there is! It's how the elevator buttons are labeled with the possible variation of using a label instead of "0".

The European elevator numbering scheme according to your own comments matches more closely with a zero-based indexing scheme than a 1-based. Or more precisely it matches my proposal to consider the numbers used to reference array elements as distances rather than indexes.

I think you misunderstand how the European numbering works. Think of it like Europeans count the separations between levels. There is no 0th separation, the first separation is the ceiling above the ground level. Saying that the ground level is the "first element" is begging the question - this is just not what Europeans count. (Well some do, but then they count similar to Americans, there is still no 0th floor ether way).

It is true that some elevators label the ground level 0, but this is usually when there are also negative levels (cellars).