> I have always seen a ruler as a discrete sequence of centimeters even if the physical object is continuous
I have trouble believing this. Does this mean you think of a ruler as a tool to assign lengths (continuous) to discrete intervals, rather than as a tool to (perhaps imprecisely) measure the (continuous) length.
for me a ruler is something that tells me how many centimeters there is in whatever it is I want to measure - but maybe it's for linguistic reasons? e.g. in french I'd say "y'a combien de centimètres là?" when measuring something long with a tape meter and someone's help, which translates to "how many centimeters are there right now?" more or less
I have trouble believing this. Does this mean you think of a ruler as a tool to assign lengths (continuous) to discrete intervals, rather than as a tool to (perhaps imprecisely) measure the (continuous) length.