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Re: Peculiarities of Pi, E, etc.
*To*: mathgroup at smc.vnet.net
*Subject*: [mg2188] Re: Peculiarities of Pi, E, etc.
*From*: Jack Goldberg <jackgold at math.lsa.umich.edu>
*Date*: Fri, 13 Oct 1995 02:24:09 -0400
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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