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?
Seems ill-posed to me. Please clarify. What exactly are your criteria for including or excluding a topic as mathematics?
Regardless, surely most people reading this board understand that the study of computation is in fact the study of transformations of (finite) symbolic representations by a finite set of well-defined rules. A such it meets criteria A, C, & D always, B sometimes. Axioms that apply include logical axioms and axioms of set theory relevant to finite sets, at minimum.