This is similar to the idea that a number isn't always a number. A number can be categorical, in which case comparison operators don't make any sense. They can be a label or a name, in which case addition or other mathematical operators don't make any sense. The same way a number can be an address, which has its own sets of operations that operate on the idea of an address.As an example, statistics has the idea of ordinal values vs interval values, where they have different properties that make them not comparable to each other and shouldn't be mistakenly be confused when working on them.
melvinroest|5 years ago
I view things like the quadratic formula as little software programs. I view complex numbers as the necessary "software system" to allow for negative square roots.
Other views I have on mathematics look at this perspective and shout "blasphemy! How could you insult such an intellectual pursuit!". But it works quite well for in me when I'm doing math.
I like your lesson. I never saw it that clearly. And with respect to numbers, I don't think I saw this at all.