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Re: Peculiarities of Pi, E, etc.



Hi Group;

In a lecture that I recently gave to my class in Mma
I mentioned that  Pi, E, EulerGamma and Catalan have 
heads Symbol and so Mma does not recognize them as 
numbers; witness  NumberQ[Pi] returns False.  To my 
suprise I noticed that Positive[Pi] returns True. 
This got me thinking and I tried a few experiments. 
Here are some of the results.

	D[Pi^5,Pi]  returns 5 Pi^4

	Integrate[E,{E,0,1}] returns  1/2

	Sum[Pi, {Pi,1,3}]  returns  6

This is strange indeed.  It confirms a suspicion I have 
harbored since learning the rudiments of Mma that the 
treatment of these so-called "mathematical" constants
(in contrast to some other kind of constants?) is 
inconsistent and confusing.  I refrain from offering 
suggestions on how to do this because I'm reasonable 
confident that no systematic change of this sort is 
easy to do.  

Before you think I`m one of those people who pick on 
Mma for every little blemish, let me quickly report 
that Maple suffers from this same ailment!  
I have not tried Derive.   
Maybe there's more to this than meets my eye?

Jack
  



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