That is a good point, and it makes sense to think of it that way. However I think that it can also be a bit "dangerous" to think too much in terms of the proper

That is a good point, and it makes sense to think of it that way. However I think that it can also be a bit "dangerous" to think too much in terms of the properties of the numbers when working with software due to the fact that for example arbitrary floats cannot be precisely represented in a limited amount of bits like we have in computers. I already hold the view that the numbers we are dealing with when working on computers are an incomplete representation of the ideals of ℝ and ℂ and their likes, so to me then it is ok to reason about code in terms of properties that stem from the language in use.