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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?
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