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Re: notation using # with exponents and &

• To: mathgroup at smc.vnet.net
• Subject: [mg93160] Re: notation using # with exponents and &
• From: AES <siegman at stanford.edu>
• Date: Wed, 29 Oct 2008 05:49:56 -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:

> 
> I don't see that what Mathematica defines as a pure function is
> inconsistent with the Wikipedia definition. For example,
> 
> f = #^2&
> 
> Always returns the same value for the same argument and has no
> I/O side effect, meeting both requirements for Wikipedia's
> definition of a pure function.

I guess I get confused, or led astray, by exactly how the words in the 
Wiki definition are to be interpreted.  For example

   f = #^x &

seems to me to be a function with an argument (the "#"), and a -- what 
shall we call it? -- a "parameter" (the "x"); and this construct returns 
_different_ values depending on how the value of x is pre-set, or 
changed, before calling it.  

In other words, it does _not_ always return the same value for the same 
argument.

I can see  #1^#2 & as evidently a pure function.  But if the function 
definition also contains parameters that can be varied, is it still a 
pure function?  And if so, what does "pure" really mean?