From: tkoenig@netcologne.de   
      
   Are there mathematical axioms for physical units and dimensional   
   analysis?   
      
   We know that you cannot just add a velocity to a time.   
      
   Everybody just applies the rules of mathematics and calculus   
   to variables with units without giving it a second thought.   
   For example, "clearly", the derivative with respect to t of   
   a*sin(omega*t) is a*omega*cos(omega*t).   
      
   And the indefinite integral of 1/T over T, where T is a themperature,   
   is ln(T) + C, correct?  Well, not really, since you cannot have   
   the logarithm of anything with a physical unit, and it is best   
   for your piece of mind if you just rewrite that as ln(T/T0),   
   where T0 takes the place of the arbitrary constant in integration.   
      
   Mathematicians have developed a very rigid theoretical system around   
   (dimensionless) numbers, but seem quite uninterested in units.   
      
   There is the Buckingham pi theorem with its associated proof.   
   This is based on what I learned at university as the "Bridgman's   
   axiom", that physical relationships cannot depend on the unit   
   system (although that name appears to be uncommon).   
      
   So, did anybody do further work on formalizing this?   
      
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