> 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 always seen a ruler as a discrete sequence of centimeters even if the physical object is continuous
> what does it say that you just called it the 1st inch, not the 0th?
but it's literally what I'm saying aha. The index of the first element is zero, even on basic household objects.