Prompted by two clever recent notes1,2 on numbers in physics teaching, I want to aggregate a couple of instructional remarks on this theme. The didactic interest in this topic could simply be to make a necessary distinction between signs and numbers.
There are “numbers” that are not numbers, that is, they do not belong to any of the known sets of numbers that mathematics teaches us, for example, a phone or social security card “number.” To be simple, these “numbers” do not permit us to add or perform any of the common arithmetic operations. In these cases, the numbers are merely signs. In a different way, all numbers we ascribe to experimental results are not really “exact” numbers. Instead, they describe intervals, that is, a range of values estimated to represent the “true” value. In other words, all measurements must indicate their estimated error. This point is usually treated...