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Re: notation using # with exponents and &

• To: mathgroup at smc.vnet.net
• Subject: [mg93182] Re: notation using # with exponents and &
• From: Bill Rowe <readnews at sbcglobal.net>
• Date: Thu, 30 Oct 2008 02:02:23 -0500 (EST)

On 10/29/08 at 5:49 AM, siegman at stanford.edu (AES) wrote:

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

>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.

Changing the value of a function parameter changes the function
into another function. That is, surely you are not suggesting
f(x) = 2 x is the same function as g(x) = 4 x even though both g
and f can be seen as instances of h(x) = a x.

if you wish to consider a parametrized function as a single
function for all values to the parameter, then you have to
regard this as a function with two arguments, the parameter and
the variable. Adding a parameter to a pure function doesn't
alter its status as a pure function using either the Wikipedia
definition or the Mathematica definition.