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Another way to say it is that 2cm * 3cm is shorthand for (2)(1cm)(i) * (3)(1cm)(j). We are complecting 3 semantics: measure and unit (which compose a module, in vector terms) and “meaning” (dimension, in vector terms).

This is why in high school physics you are taught to always write down the units of each number: typing them helps avoid a big amount of errors.

Note that “typing” and “vector terms” are not essential, just helps me express it with the HN crowd easily.



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