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Topic: Sixth grade math
Replies: 115   Last Post: Feb 15, 2010 5:36 AM

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ostap_bender_1900@hotmail.com

Posts: 681
Registered: 2/1/08
Re: Sixth grade math
Posted: Feb 4, 2010 7:50 PM
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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?

http://en.wikipedia.org/wiki/Function_(mathematics)

More precisely, if ? is a function from a X to Y, and S is any subset
of X, the restriction of ? to S is the function ?|S from S to Y such
that ?|S(s) = ?(s) for all s in S

>
> Brouwer, who gave us the fixed point theorem, also gave
> us the deeper result: all real functions are continuous.
>


Excuse me? What do you mean by "real functions"?



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