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.