Lou Talman says:
That's a very good question. How does one handle units in general? What axioms does one use? If there are none, then Robert's earlier question about an exam is well-posed: "Is this mathematics?"
Hmmm, this seems easy to parse, but the options all seem absurd. Is mathematics [A] only that which deduces conclusions from logic, axioms, and rules of inference?
[B] Is it the study of "units"? [C] Is it the study of those two things together? [D] Is it the study of either of those two, together or alone?
Keep in mind that Lou misstated what I said (probably unintentionally). I was referring to that proof test in the document I referenced. It showed a proof and then asked "On a scale of 1 to 5, how strongly do you agree or disagree with this proof?"
I paraphrased all of that into "Does this look like mathematics? Good, you Pass."
In other words, all the test was doing was showing students mathematical stuff and asking them how strongly they agreed that it was mathematical stuff. I wasn't asking "Is this test mathematics?" I already knew the answer to that. No.
Consider: (x + 2)(x - 2) = x^2 -4x + 4
1. Strongly agree
2. Somewhat agree
3. Not sure
4. Somewhat disagree
5. Strongly Disagree