An Axiomatic Approach to Dimensions in Physics
Micheal Parkinson · American Journal of Physics · 1964
A set of axioms and a formalism is presented for handling units and dimensions. Using the axioms, one form of the II theorem is proved simply and rigorously; also, two often debated questions are given definitive answers, both in the affirmative: (1) Are transcendental functions of a dimensional quantity legitimate? (2) Are the laws of physics always expressible in a form invariant under transformations of units?