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

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T.H. Ray

Posts: 1,107
Registered: 12/13/04
Re: Sixth grade math
Posted: Feb 12, 2010 8:40 AM
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Ostap Bender wrote

> On Feb 11, 4:57 am, "T.H. Ray" <thray...@aol.com>
> wrote:

> > Ostap Bender wrote
> >

> > > On Feb 10, 4:36 am, "T.H. Ray" <thray...@aol.com>
> > > wrote:

> > > > Ostap Bender wrote
> >
> > > > > On Feb 9, 4:02 am, "T.H. Ray"
> <thray...@aol.com>
> > > > > wrote:
> > > > > > Ostap Bender wrote
> >
> > > > > > > On Feb 8, 4:15 am, "T.H. Ray"
> > > <thray...@aol.com>
> > > > > > > wrote:
> > > > > > > > Ostap Bender wrote
> >
> > > > > > > > > On Feb 7, 2:11 am, "T.H. Ray"
> > > > > <thray...@aol.com>
> > > > > > > > > wrote:
> > > > > > > > > > Ostap Bender wrote
> >
> > > > > > > > > > > On Feb 6, 5:41 am, "T.H. Ray"
> > > > > > > <thray...@aol.com>
> > > > > > > > > > > wrote:
> > > > > > > > > > > > Ostap Bender wrote
> >
> > > > > > > > > > > > > On Feb 5, 11:11 am, "T.H.
> Ray"
> > > > > > > > > <thray...@aol.com>
> > > > > > > > > > > > > wrote:
> > > > > > > > > > > > > > MoeBlee wrote
> >
> > > > > > > > > > > > > > > On Feb 5, 10:50 am, "T.H.
> > > Ray"
> > > > > > > > > > > <thray...@aol.com>
> > > > > > > > > > > > > > > wrote:
> >
> > > > > > > > > > > > > > > > Speaking only for my
> own
> > > > > > > > > characterization,
> > > > > > > > > > > I
> > > > > > > > > > > > > find
> > > > > > > > > > > > > > > no
> > > > > > > > > > > > > > > > conflict between the
> set
> > > > > theoretic
> > > > > > > > > > > definition
> > > > > > > > > > > > > and
> > > > > > > > > > > > > > > > mine.
> >
> > > > > > > > > > > > > > > What was your particular
> > > > > > > characterization
> > > > > > > > > > > again?
> > > > > > > > > > > > > If
> > > > > > > > > > > > > > > it's not
> > > > > > > > > > > > > > > extensional then it's in

> > > conflict
> > > > > > > with
> > > > > > > > > the
> > > > > > > > > > > set
> > > > > > > > > > > > > > > theoretic definition.
> >
> > > > > > > > > > > > > > It's both extensional and
> > > > > > > > > intensional--though
> > > > > > > > > > > > > > incomplete, as I pointed
> > > out--to
> > > > > define
> > > > > > > > > > > function as
> > > > > > > > > > > > > the
> > > > > > > > > > > > > > transformation of one set
> of
> > > > > numbers to
> > > > > > > > > > > another.
> > > > > > > > > > > > >  The
> > > > > > > > > > > > > > property of relation
> inheres in
> > > > > every
> > > > > > > > > function.
> >
> > > > > > > > > > > > > > > In ordinary mathematics,
> one
> > > may
> > > > > be
> > > > > > > > > called to
> > > > > > > > > > > > > prove
> > > > > > > > > > > > > > > that something
> > > > > > > > > > > > > > > (call it 'C') is or is

> not a
> > > > > > > function,
> > > > > > > > > and
> > > > > > > > > > > the
> > > > > > > > > > > > > way to
> > > > > > > > > > > > > > > do that is show
> > > > > > > > > > > > > > > that C is or is not a

> > > relation
> > > > > such
> > > > > > > that
> > > > > > > > > for
> > > > > > > > > > > all
> > > > > > > > > > > > > x,
> > > > > > > > > > > > > > > y, z, if <x y> and
> > > > > > > > > > > > > > > <x z> in C, then y=z. On

> the
> > > > > other
> > > > > > > hand,
> > > > > > > > > with
> > > > > > > > > > > > > these
> > > > > > > > > > > > > > > various informal
> > > > > > > > > > > > > > > definitions, what even IS

> the
> > > > > > > > > mathematical
> > > > > > > > > > > (and
> > > > > > > > > > > > > > > compatible with
> > > > > > > > > > > > > > > classial mathematics, as

> that
> > > is
> > > > > the
> > > > > > > > > context
> > > > > > > > > > > of
> > > > > > > > > > > > > the
> > > > > > > > > > > > > > > ordinary
> > > > > > > > > > > > > > > mathematics a

> sixth-grader
> > > will
> > > > > go on
> > > > > > > to
> > > > > > > > > > > study in
> > > > > > > > > > > > > > > college) means that
> > > > > > > > > > > > > > > one would prove that

> > > something is
> > > > > or
> > > > > > > is
> > > > > > > > > not a
> > > > > > > > > > > > > > > function?
> >
> > > > > > > > > > > > > > Sure.  See my explanation
> to
> > > Ostap
> > > > > > > Bender
> > > > > > > > > as to
> > > > > > > > > > > why
> > > > > > > > > > > > > > his description that
> assigns
> > > > > properties
> > > > > > > is
> > > > > > > > > not
> > > > > > > > > > > a
> > > > > > > > > > > > > > function, absent a relation
> > > between
> > > > > > > sets.
> >
> > > > > > > > > > > > > Which explanation? Of which
> > > > > description?
> >
> > > > > > > > > > > > > Are you saying that my
> relation
> > > f: C
> > > > > ->
> > > > > > > Q,
> > > > > > > > > where
> > > > > > > > > > > C =
> > > > > > > > > > > > > {New York, San
> > > > > > > > > > > > > Francisco, Los Angeles} and f

> =
> > > {{New
> > > > > > > York,
> > > > > > > > > 35},
> > > > > > > > > > > (San
> > > > > > > > > > > > > Francisco, 55),
> > > > > > > > > > > > > {Los Angeles, 70}} is NOT a

> > > function?
> > > > > > > Why?
> >
> > > > > > > > > > > > Better to ask you, why you
> think it
> > > > > _is_ a
> > > > > > > > > > > function,
> > > > > > > > > > > > since I have already explained
> why
> > > not.
> >
> > > > > > > > > > > I am sorry but I never saw how
> > > anything
> > > > > you
> > > > > > > wrote
> > > > > > > > > > > proves that the
> > > > > > > > > > > above is not a function.

> >
> > > > > > > > > > > >  What properties
> > > > > > > > > > > > of a function do you think this

> > > > > assignment
> > > > > > > of
> > > > > > > > > > > values
> > > > > > > > > > > > has?  I need to know what you
> do
> > > not
> > > > > > > understand
> > > > > > > > > of
> > > > > > > > > > > my
> > > > > > > > > > > > previous explanation.
> >
> > > > > > > > > > > I am an old-fashioned man and
> still
> > > > > operate
> > > > > > > under
> > > > > > > > > the
> > > > > > > > > > > following
> > > > > > > > > > > definitions:

> >
> > > > > > > > > > > From Wiki:
> >
> > > > > > > > > > > In mathematics, a function is a
> > > relation
> > > > > > > between
> > > > > > > > > a
> > > > > > > > > > > given set of
> > > > > > > > > > > elements called the domain and a

> set
> > > of
> > > > > > > elements
> > > > > > > > > > > called the codomain.
> > > > > > > > > > > The function associates each

> element
> > > in
> > > > > the
> > > > > > > > > domain
> > > > > > > > > > > with exactly one
> > > > > > > > > > > element in the codomain.

> >
> > > > > > > > > > > A binary relation f between two
> sets
> > > A
> > > > > and B
> > > > > > > is a
> > > > > > > > > > > subset of A × B.
> >
> > > > > > > > > > > Thus, as Bill Dubuque puts it, a
> > > function
> > > > > f:
> > > > > > > A ->
> > > > > > > > > B
> > > > > > > > > > > is a single-valued
> > > > > > > > > > > total binary relation between

> sets A
> > > and
> > > > > B.
> >
> > > > > > > > > > The set-theoretic definition of
> > > function
> > > > > > >  demands a
> > > > > > > > > > relation that allows transforming a
> set
> > > of
> > > > > > > values
> > > > > > > > > into one
> > > > > > > > > > common value.
> >
> > > > > > > > > What does this mean?
> >
> > > > > > > > > BTW, why do you like the term "to
> > > transform"
> > > > > so
> > > > > > > much?
> > > > > > > > > "To transform"
> > > > > > > > > means "to change", doesn't it? Do all

> > > > > functions
> > > > > > > > > actually change their
> > > > > > > > > domains? I just don't see that as a

> good
> > > > > > > metaphor.
> >
> > > > > > > > It isn't a metaphor at all.  It's a
> > > property
> > > > > that
> > > > > > > > inheres in every function.  It's a
> > > necessary
> > > > > > > condition.
> >
> > > > > > > Necessary condition for what? Could you
> > > please
> > > > > give
> > > > > > > precise
> > > > > > > mathematical definitions of what you are

> > > talking
> > > > > > > about?
> >
> > > > > > If you don't know what the logical terms
> > > necessary
> > > > > and
> > > > > > sufficient mean, I can't help you.
> >
> > > > > Is it necessary for you to act as an
> insulting
> > > > > jackass? Suffices to
> > > > > say that I have been familiar with the terms
> > > > > necessary and sufficient
> > > > > since 8th grade.

> >
> > > > Good.  And I didn't mean to be insulting.
>  Sorry.
> >
> > > > > What I referred to is your sentence:
> >
> > > > > > > >  It's a necessary condition.
> >
> > > > > If you were so much more of a logician than
> I,
> > > you
> > > > > would know that
> > > > > when you say that something is "a necessary
> > > > > condition", you must
> > > > > specify FOR WHAT it is a necessary condition.

> >
> > > > It seems I have to keep repeating myself.  I
> > > thought
> > > > I was clear that function was not defined until
> the
> > > > (necessary)relation between setsw as defined.
> >
> > > "Clear" is the last word I and most other people
> here
> > > would apply to
> > > your exposition of your own thoughts. Your
> > > explanations are the most
> > > cryptic I have ever seen.

> >
> > Then I wager you haven't seen enough.  Or very far.
> >

>
> NO, I've seen more than enough. However, when I
> encountered cryptic
> passages and asked their authors for clarifications,
> the vast majority
> went out of their way to make themselves understood.
> You, on the other
> hand, make no effort at all to answer such questions.
> On the contrary,
> I get the feeling that to you, the fact that I and
> others don't often
> understand what you are saying is a badge of honour:
> proof that you
> are smarter than others.
>

I am not smarter than others, nor do I have a need
to try and prove same. I regret that I seem obscure,
and I think I have provided sufficient references for
one to avoid having to take my word for anything. Your
charge that I do not attempt to answer, however, is
unfounded.

> >
> > > > > > > > The range of values within the domain
> have
> > > to
> > > > > obey
> > > > > > > > a relation between sets that defines
> the
> > > > > function.
> >
> > > > > > > Hoe does all this relate to what I wrote:
> >
> > > > > > > ""To transform" means "to change",
> doesn't
> > > it? Do
> > > > > all
> > > > > > > functions
> > > > > > > actually change their domains? I just

> don't
> > > see
> > > > > that
> > > > > > > as a good
> > > > > > > metaphor.

> >
> > > > > > > Take, for example, the function Y that
> maps
> > > > > people to
> > > > > > > their eye
> > > > > > > colour. Does Y transform me into an eye

> > > colour? I
> > > > > > > don't think so. I
> > > > > > > don't feel transformed. I still feel like

> a
> > > man,
> > > > > not
> > > > > > > a colour.
> >
> > > > > > I'm afraid your concrete thinking won't get
> you
> > > to
> > > > > the
> > > > > > abstract meaning of function.  Your
> particular
> > > eye
> > > > > > color has nothing to do with the set of the
> > > > > population
> > > > > > that maps to the set of eye colors
> distributed
> > > > > among the
> > > > > > population.
> >
> > > > > What is this "set of the population" that you
> > > refer
> > > > > to?
> >
> > The set of people with eyes.
> >

>
> OK, so let's substitute this term "the set of people
> with eyes" into
> your original sentence:
>
> "Your particular eye color has nothing to do with the
> set of people
> with eyes that maps to the set of eye colors
> distributed among the
> population."
>
> Do you think this is a clear and understandable
> sentence?
>

Well, it is to me.

> What does the phrase ""Your particular eye color has
> nothing to do
> with the set of people with eyes" mean? Why is is of
> any relevance?
>

Because it differentiates the abstract map between
sets from your concrete membership in the set. Remember,
my whole original point was to avoid concrete
connotations associated with the definition
of "function," in favor of a simple abstraction on which
one could build toward more comprehensive and compact
expressions. Then by the time one gets to "single
valued total relation between sets," the definition is as
rich and meaningful as it should be.

> >
> > > > Yes, but you're leaving out the necessary
> relation
> > > > between sets that allows a mapping. If those
> terms
> > > of
> > > > existence were not important, any relation
> would be
> > > a
> > > > function.
> >
> > > But how does your general amorphous paragraph
> above
> > > relate to the "eye
> > > colour" function? Can't you be concrete?

> >
> > I could, but as I have said and implied: function

> is
> > not a concrete concept.  In fact, that is what
> started
> > this row in the first place--I objected to the use
> of
> > terms like machine and black box to describe
> "function"
> > to those just learning, because even though useful,
> the
> > terms don't capture the meaning of a mathematical
> act
> > that demands an abstract relation between sets.
>  For the
> > same reason, I object to the unsubtle treatment of
> > definitions that employs the symbols as concrete

> objects
> > that stand for themselves and nothing more.  Of
> course,
> > the usual suspects have come forth to ridicule and
> > berate me for that view--thoughtful people can

> judge for
> > themselves its validity.
> >
> > I think, however, that you have served as an

> example of
> > what harm comes from a pedagogy that stresses
> content
> > over meaning.  The "memorize this, use it and stop
> > questioning" school of mathematics has certainly

> created
> > a lasting scar on the community and on the art. I
> favor
> > a program that aims for higher levels of
> abstraction,
> > continuously.  
> >

>
> I am with you. Certainly, if whatever you are trying
> to teach us is
> important and of substance, then I am all for
> learning it. My problem
> is that I cannot understand a single sentence of your
> explanations.
> You say that what my professors taught me in college
> and graduate
> school was "memorize this, use it and stop
> questioning". Well, at
> least I understood what my professors were saying.


How would I know what your professors taught you? My
comment, actually, was directed at the primary and
secondary school level, and comes from personal
experience.

> I
> don't understand
> what YOU are saying.
>

Sorry.
> >
> > > > > Somehow I feel that you are avoiding
> precision on
> > > > > purpose. I fail to
> > > > > se why a person would make no effort to make

> > > himself
> > > > > to be understood
> > > > > by others.

> >
> > > > > One of the most influential films that I saw
> in
> > > > > childhood had the
> > > > > following episode. The students were to write

> a
> > > > > composition titled
> > > > > "What is Happiness". The hero's composition

> > > consisted
> > > > > of only one
> > > > > sentence: "Happiness is when you are

> understood".
> >
> > > > It's a rather brash extrapolation, isn't it,
> that
> > > > because you do not understand me, no one does.
> >
> > > Am I the only one here in this thread who says
> that
> > > they find you hard
> > > to understand? Just look around.

> >
> > Never read Thoreau, did you?  Just a hunch.
> >

>
> And my hunch is that you have never read Bulgakov or
> Pilevin. But how
> does this relate to our conversation? Or are you
> again trying to
> proove your intellectual superiority?


You might have googled Thoreau and learned the relevance,
if you were curious enough. If you aren't, you could
just ignore it. But to assign motives to me merely from
your personal belief is overreaching.

Tom


Date Subject Author
1/25/10
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Read Re: Sixth grade math
T.H. Ray
2/8/10
Read Re: Sixth grade math
ostap_bender_1900@hotmail.com
2/8/10
Read Re: Sixth grade math
T.H. Ray
2/10/10
Read Re: Sixth grade math
Michael Stemper
2/10/10
Read Re: Sixth grade math
T.H. Ray
2/10/10
Read Re: Sixth grade math
victor_meldrew_666@yahoo.co.uk
2/10/10
Read Re: Sixth grade math
T.H. Ray
2/10/10
Read Re: Sixth grade math
T.H. Ray
2/11/10
Read Re: Sixth grade math
victor_meldrew_666@yahoo.co.uk
2/11/10
Read Re: Sixth grade math
T.H. Ray
2/8/10
Read Re: Sixth grade math
Marshall
2/8/10
Read Re: Sixth grade math
T.H. Ray
2/8/10
Read Re: Sixth grade math
Marshall
2/9/10
Read Re: Sixth grade math
T.H. Ray
2/8/10
Read Re: Sixth grade math
ostap_bender_1900@hotmail.com
2/9/10
Read Re: Sixth grade math
T.H. Ray
2/9/10
Read Re: Sixth grade math
ostap_bender_1900@hotmail.com
2/8/10
Read Re: Sixth grade math
ostap_bender_1900@hotmail.com
2/9/10
Read Re: Sixth grade math
T.H. Ray
2/9/10
Read Re: Sixth grade math
ostap_bender_1900@hotmail.com
2/10/10
Read Re: Sixth grade math
T.H. Ray
2/10/10
Read Re: Sixth grade math
ostap_bender_1900@hotmail.com
2/11/10
Read Re: Sixth grade math
T.H. Ray
2/11/10
Read Re: Sixth grade math
ostap_bender_1900@hotmail.com
2/12/10
Read Re: Sixth grade math
T.H. Ray
2/12/10
Read Re: Sixth grade math
Brian Q. Hutchings
2/12/10
Read Re: Sixth grade math
ostap_bender_1900@hotmail.com
2/12/10
Read Re: Sixth grade math
ostap_bender_1900@hotmail.com
2/13/10
Read Re: Sixth grade math
victor_meldrew_666@yahoo.co.uk
2/14/10
Read Re: Sixth grade math
ostap_bender_1900@hotmail.com
2/15/10
Read Re: Sixth grade math
ostap_bender_1900@hotmail.com
2/12/10
Read Re: Sixth grade math
Brian Q. Hutchings
2/9/10
Read Re: Sixth grade math
Brian Q. Hutchings
2/9/10
Read Re: Sixth grade math
ostap_bender_1900@hotmail.com
2/10/10
Read Re: Sixth grade math
ostap_bender_1900@hotmail.com
2/10/10
Read Re: Sixth grade math
Brian Q. Hutchings
2/10/10
Read Re: Sixth grade math
ostap_bender_1900@hotmail.com
2/10/10
Read Re: Sixth grade math
ostap_bender_1900@hotmail.com
1/28/10
Read Re: Sixth grade math
Frederick Williams
1/28/10
Read Re: Sixth grade math
Jack Markan
1/28/10
Read Re: Sixth grade math
Dave L. Renfro
1/28/10
Read Re: Sixth grade math
Porky Pig Jr
1/28/10
Read Re: Sixth grade math
Jack Markan
1/29/10
Read Re: Sixth grade math
Michael Stemper
1/29/10
Read Re: Sixth grade math
Jack Markan
1/28/10
Read Re: Sixth grade math
Jack Markan

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