ordinally, not cardinally. Ordinal means Order, Cardinal means Size. And choosing "0" to mean "absent" is as arbitary and misguided (unless you are optimizing

ordinally, not cardinally. Ordinal means Order, Cardinal means Size. And choosing "0" to mean "absent" is as arbitary and misguided (unless you are optimizing bits and cycles on a low-powered machine) as choosing "-1" to mean "absent"