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Re: notation using # with exponents and &

• To: mathgroup at smc.vnet.net
• Subject: [mg93150] Re: notation using # with exponents and &
• From: AES <siegman at stanford.edu>
• Date: Wed, 29 Oct 2008 05:48:08 -0500 (EST)
• Organization: Stanford University
• References: <ge6nik$ll4$1@smc.vnet.net>

In article <ge6nik$ll4$1 at smc.vnet.net>,
 Bill Rowe <readnews at sbcglobal.net> wrote:

> In any case, whether what the Mathematica documentation calls a
> pure function is consistent with some other definition is of
> little practical significance. It certainly isn't helpful to
> call the construct an anonymous function even if this is more
> correct in some sense given doing so is not consistent with the
> Mathematica documentation. Using a nomenclature inconsistent
> with the documentation is certain to cause more confusion rather
> than increase clarity.

I'm afraid I'd flatly disagree with nearly every statement in this 
paragraph:

1)  Suppose a reasonably widely accepted definition for any technical 
term or 'term of art' -- such as the term "pure function", for example 
-- exists and is widely used and understood in the mathematical world 
(and I've already stated that I'm no expert on the concept of a pure 
function).

Then it certainly seems to me that Mathematica would, and _should_, want 
to conform to that accepted usage, if at all possible.  (And if, for 
some good and sufficient reason, they chose to diverge from the accepted 
usage, it would help M users if they state this very clearly, and maybe 
say why they're choosing to redefine the term.)

2)  Calling the construct under discussion an "anonymous function" might 
or might not be the optimum choice -- I don't claim to know -- but it 
would at least focus attention on what seems to be a major distinction 
for the construct -- that it need not have a name, and can be used 
without every being named.

3) "Using a nomenclature inconsistent with the documentation is certain 
to cause more confusion rather than increase clarity."  Well, duh!!!

Is using a nomenclature that is inconsistent _with the established or 
already widely accepted mathematical nomenclature for some concept or 
construct_ likely to increase clarity and decrease confusion among users?