The abstract unit-inch is of equal length across any part of the ruler. A reordering of the twelve inch-units produces the same ruler. This has great utility because it is not always possible to start measuring from the end of the ruler. The inch is the concretization of the unit. We go beyond merely asserting the exchangeability of units, we demonstrate it through their concrete realization.
Concrete units operationalize additivity.
Obtaining total length by concatenating inches demonstrates that additivity holds. Since combining inches by physical concatenation gives the result predicted by additivity, rulers implement what Physicist Norman Campbell called fundamental measurement. We count by means of the ordered numerals to obtain the total. Rulers implement a correspondence between units and numbers. The left-most edge or marker of the ruler is the beginning and indicates the absence of any units, i.e., none.