> Van: [email protected] > [mailto:[email protected]] Namens Raul Miller > Verzonden: maandag 17 december 2012 16:44 > Aan: Chat forum > Onderwerp: Re: [Jchat] [Jgeneral] Power Conjuntion > > [moving to chat, because this is not relevant to the general forum.] > > The relationship you described creating, here, is deterministic after > it exists. And, when it does not exist, it's not a function.
Wrong again. A relationship can be given as a pair of items of which each first item is unique. Or as a prescription, formula, algorithm which can produce such pairs, just like x --> x^2 is a function without given all the pairs. So the relation I describe, invoke a random generator, does exist, although it is unknown. But mathematics is full of functions (most of) the values of which are unknown. Or do you consider Ackermann's function not to be a function since we have only a few values? Your different view perhaps comes from the fact that you want a function to have a fixed output, given the input. But that is not what the definition implies. At least, in my opinion. Since the rest is (probably) semantics, my interest is declining rapidly . R.E. Boss > On Mon, Dec 17, 2012 at 10:24 AM, R.E. Boss <[email protected]> wrote: > > From your link I read > > "In mathematics, a function is a relation between a set of inputs and a set > > of permissible outputs with the property that each input > > is related to exactly one output." > > That is equivalent to the definition of function I also had in mind. > > > > If I invoke a random generator n times I have a relation between i.n and > > the outputs, so I got a non-deterministic function. > > In general, any array of items is a function, deterministic or not. > > So your statement that " anything with non-deterministic results cannot be > > a function" is not true. QED. > > > > > > R.E. Boss > > > > > >> -----Oorspronkelijk bericht----- > >> Van: [email protected] > >> [mailto:[email protected]] Namens Raul Miller > >> Verzonden: maandag 17 december 2012 15:31 > >> Aan: [email protected] > >> Onderwerp: Re: [Jgeneral] Power Conjuntion > >> > >> It's true for the mathematical meaning of 'function' -- see > >> http://en.m.wikipedia.org/wiki/Function_(mathematics) for an example of > >> this kind of thinking. > >> > >> That said, you can transform a nondeterministic relationship into a > >> determistic function by supplying parameters sufficient to represent the > >> nondetermanism. > >> > >> Or, were you speaking of something else? > >> > >> -- > >> Raul > >> > >> On Monday, December 17, 2012, R.E. Boss <[email protected]> wrote: > >> > > >> > > >> >> -----Oorspronkelijk bericht----- > >> >> Van: [email protected] [mailto: > >> [email protected]] Namens Raul Miller > >> >> Verzonden: zondag 16 december 2012 21:07 > >> >> Aan: [email protected] > >> >> Onderwerp: Re: [Jgeneral] Power Conjuntion > >> >> > >> >> Actually, anything with non-deterministic results cannot be a > >> >> function. (...) > >> >> > >> > > >> > > >> > This is not true. > >> > > >> > > >> > R.E. Boss > >> > > >> > > >> > > >> > > >> > > >> > ---------------------------------------------------------------------- > >> > For information about J forums see http://www.jsoftware.com/forums.htm > >> > > >> ---------------------------------------------------------------------- > >> For information about J forums see http://www.jsoftware.com/forums.htm > > > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
