[joehilton]

The difference between the amount and a number is exactly what I'm afraid negative numbers misrepresent.

Real and imaginary number sets are the heart of the point (and I think my high school calc - if I can remember that many years ago - did include some work with imaginary numbers, certainly by early college work).

Since an amount can never be negative, then a negative number only makes sense to denote the movement of an amount from one system to another. If we say that negative numbers are real numbers, and especially if we use them as the same class as positive numbers when building blocks to formulate ideas and theories about physical properties and amounts, I'm wondering if there is a potential downside to our fundamental understanding of what our results actually mean.

One of the other replies points out the necessity of units paired with numbers, and I think this is correct. The problem I'm observing, and the heart of my question, is that we have many, many ideas/proofs/theorems in mathematics with unitless numbers (constants and so on, both positive and negative), and then we use the results of this work to jump back into the physical universe to "prove" something. Could there be a problem with our basic use of numbers when we do this?