XPost: sci.math   
   From: fateman@cs.berkeley.edu   
      
   On 8/30/2014 9:32 AM, IV wrote:   
   > "Axel Vogt"  wrote in news:c6c8d8F6dkkU1@mid.individual.net...   
   >> I think the English article contains 'errors' (it is meant:   
   >> inverse of trigs, only)   
   > There are some slightly different definitions of Elementary functions.   
   > It depends on the objectives of the respective author.   
   >   
   >> What should "real" be? You already kick out sqrt and log,   
   >> besides inverse trigonometrics.   
   > I have "Real" capitalized. That means, it is a proper name. This refers   
   > to the functions in the Real numbers.   
   >   
   >   
      
   If you would do your homework and define explicitly   
   the meaning of your phrase "functions in the Real numbers"   
   then maybe you could expect an answer.   
      
   Given at least one interpretation, the answer is clear.   
      
   You cannot even tell if an arbitrary function f(x) composed of common   
   elementary functions is identically zero.  Thus if someone   
   told you  the solution to f(x)=0   is   x=p,  you could not   
   even check if f(p) is zero.  So you can't always solve f(x)=0.   
      
   At least not with 100% algorithmic methods over all such functions.   
      
   If you want to learn what this means, look up work by Daniel   
   Richardson in 1967-68  on decidability.   
      
   RJF   
      
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