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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.
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