From: PointedEars@web.de   
      
   Paul B. Andersen wrote:   
   > Den 03.02.2026 16:14, skrev Thomas 'PointedEars' Lahn:   
   >> Paul B. Andersen wrote:   
   >>> That the derivative of a function must be zero   
   >>> when the function is zero is indeed a weird idea.   
   >>   
   >> The problem is language.  Mathematics as a language is precise, but when   
   >> mathematics is described using natural language, that is not necessarily so.   
   >>   
   >> One must distinguish between a function that is _identically_ zero, i.e.   
   >> whose value is zero _everywhere_, and a function whose value is zero _for a   
   >> finite number of arguments in its domain_.   
   >   
   > Isn't the function f(t)≡ 0  a constant?   
      
   It is _constant_.   
      
   > Such a function would be meaningless.   
      
   No.  Consider, for example, that it could be the derivative of a constant   
   function whose value is NOT zero (everywhere).   
      
   Then if the latter is a function of time, that the former is identically   
   zero is physically meaningful.   
      
   For example, if v(t) = const., then a(t) = dv(t)/dt = 0 even if v(t) != 0.   
   Then we know that the motion is inertial in an inertial reference frame.   
      
   Or, if a(t) = const., then da(t)/dt, called "the jerk" :-D, is identically   
   zero.   
      
   Or if the function describes a conserved quantity, then its derivative with   
   respect to (proper) time is identically zero.  This is very important in   
   physics, cf. Lagrangian mechanics and Noether's Theorem.   
      
   --   
   PointedEars   
      
   Twitter: @PointedEars2   
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