Re: functions

*To*: mathgroup at smc.vnet.net*Subject*: [mg45573] Re: functions*From*: Bill Rowe <readnewsciv at earthlink.net>*Date*: Wed, 14 Jan 2004 01:26:32 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

On 1/13/04 at 4:04 AM, Harold.Noffke at wpafb.af.mil (Harold Noffke) wrote: > I think a "better answer" can be had by examining Mathematica 5.0's > ability to remain error free when confronted with cleverly constructed > known irrational expressions, such as the one below, copied from the > Built-In Functions reference for Rationals > In[1]:= Element[3^(Sqrt[5]), Rationals] > Out[1]= False This appears to be no better than the other answers since Elements[3^Sqrt[4.], Rationals] False while Elements[3^Sqrt[4],Rationals] True Clearly, any computer system can only represent irrational numbers as a finite string of digits or as a special symbol. It should be equally clear any finite set of digits can be written as the ratio of two integers. So, the only distinction between a finite set of digits intended to represent an irrational number and a rational number is intent. Since there is currently no way for Mathematica to determine your intent, it seems clear any proceedure to restrict a function to rational numbers can only work if the rational numbers are not given in decimal form. -- To reply via email subtract one hundred and four