On Feb 3, 3:48 am, "T.H. Ray" <thray...@aol.com> wrote: > Ostap Bender wrote > > > > > > I don't know about that, but to me, a function is > > an > > > > assignment of > > > > properties to the members of your set, like the > > > > weather report: > > > > > New York -> 30 degrees, snow > > > > San Francisco -> 55 degrees, rain > > > > Los Angeles -> 69 degrees, sunny > > > > > etc. > > > > Ah, now I see the difficulty. No--the set of > > cities > > > with corresponding temperature and weather > > conditions > > > are not defined by a function until you define a > > > relation among them. A simple relation to define > > the > > > function is the season of the year; If these > > initial > > > conditions exist in winter, then in summer this set > > > of numbers will change at some particular time to > > > something like > > > I was talking about the instantaneous weather report > > on the Weather > > Channel or CNN: At this moment, the temperatures are: > > > New York -> 30 degrees, snow > > San Francisco -> 55 degrees, rain > > Los Angeles -> 69 degrees, sunny > > > > New York, 78 degrees, sunny > > > San Francisco, 65 degrees, rain > > > Los Angeles, 85 degrees, partly cloudy > > > > A function necessarily transforms... > > > What do you mean by "transforms"? Does the weather > > report transform > > the set of cities into a set of temperatures? I would > > use the term > > "assigns" instead of "transforms". > > No. The weather report is the result of the function > that transforms one set of data into another. It is > certainly a transformation, not an assignment of values, > because it is not arbitrary. > > > There do exist arbitrary > assigments of values that are functions; e.g., ordering > some group of people by height. Even in such cases, > however, transformation applies--the order function > transforms a random distribution of values into an > ordered sequence. > > > > ... one set of data to > > > another. The above is an example of a continuous > > > function; > > > That would depend on your domain. If your domain is > > the Earth' surface > > - then the current temperature is continuous. if your > > domain is the > > set of 100 big cities - there can be no notion of > > continuity. > > The domain for climate is, of course, the earth's > surface and atmospheres--what else would it be? >
Many things. For example, the set of weather stations that measure the outside temperature. Any set can serve as the domain for a function.
> > The set > of cities is most certainly embedded in that surface > and their climate (by the fixed point theorem)is a > function of changes in that surface and atmosphere. >
Isn't a restricted function still a function in its own right?