From: relativity@paulba.no   
      
   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?   
   Such a function would be meaningless.   
      
   >   
   > The derivative of the former function *is* actually zero because it is a   
   > special case of a constant function, but the derivative of the latter   
   > function is not necessarily zero.   
   >   
   >> You know that sin(0) = 0   
   >   
   > Yes.   
   >   
   >> and dsin(0)/dt = cos(0) = 1   
   >   
   > No.   
   >   
   >    dsin(0)/dt = d(0)/dt = 0.   
      
   You are obviously right.   
      
   >   
   > But   
   >   
   >    dsin(t)/dt|_{t=0} := [dsin(t)/dt](0) = cos(0) = 1.   
   >   
      
   This was what I meant. Sloppy!   
      
   --   
   Paul   
      
   https://paulba.no/   
      
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