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?