I've seen this claim throughout the site about observables in nature being continuous. Where did that come from? It isn't really true and doesn't contribute anything to the mathematics. People frequently ask questions like "how many chairs are in the living room?" One normally expects an integer answer to such a question. Only a pedant (or wise guy) would respond "2 1/2" (because perhaps one chair is straddling the dividing line between living room and dining room at that particular moment).