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Topic: Paul Lutus says dumb things
Replies: 107   Last Post: Dec 11, 2001 12:30 PM

 Messages: [ Previous | Next ]
 Adam Ringler Posts: 36 Registered: 12/13/04
Re: Paul Lutus says dumb things
Posted: Dec 2, 2001 2:48 PM

What is so bad about the extended reals, they seem like a fine system of
numbers to work with to me, you just have to remember the properties of oo
and -oo.

Cheers,
"Chan-Ho Suh" <csuh@math.ucla.edu> wrote in message
news://3C099B3D.8A447554@math.ucla.edu...
>
>
> Paul Lutus wrote:
>

> > "Chan-Ho Suh" <csuh@math.ucla.edu> wrote in message
> > news://3C082CE3.B54ECB73@math.ucla.edu...
> >

> > > Lutus is incorrect.
> >
> > Post your erroneous argument first.

>
> I have posted no erroneous argument, nor do I intend to ever do so.
>

> >
> >

> > > The equal sign refers to equality of numbers.
>
> [gibberish snipped]
>
>

> >
> > The example under discussion --
> >
> > lim x -> 0, 1/x = infinity
> >

>
> Oh, you're doing the "I'm wrong but don't want to admit it so I'll change

the
> discussion topic" approach. Note that 0 and infinity were switched in the
> original post I responded to.
>
>

> >
> > -- is an unfortunate shorthand that appears to say:
> >
> > "as x approaches the limit of zero, 1/x equals infinity"
> >
> > -- which, of course, is false and is not what a limit represents.
> >

>
> In the extended reals (one or two point compactifications) this makes

perfect
> sense. It is not the working mathematician's fault that some calculus
teachers
> are afraid to talk about the concept of points at infinity.
>
>

> >
> > > The left hand
> > > side is a limit of (presumably) the real function 1/x as x approaches

> > infinity and
> > > so is precisely the real number 0..
> >
> > You are looking at the wrong example. Read above.
> >

>
> I'm looking at the example that started the thread. Do *you* know how to

>
>

> >
> > > The right hand side is (the way I am reading
> > > it) the real number 0. Clearly 0 = 0. The thing to remember here is

that
> > the
> > > limit operator returns a number (assuming the operator is well-defined
and
> > perhaps
> > > assuming +/- infinity to be an 'extended' number).
> > >
> > > Lutus' mistake is common.

> >
> > Yours is much more common. You have overlooked this semantic ambiguity

in
> > the limit expression, the bane of math teachers.
> >

>
> Yours is the most common mistake: taking one's limited knowledge to be
> all-encompassing. This business of 'extended' reals is the bane of math
> teachers who never understood the subject.
>
>

Date Subject Author
11/30/01 Lou Tuss
11/30/01 Gregory L. Hansen
11/30/01 Chan-Ho Suh
11/30/01 Jake
11/30/01 Paul Lutus
11/30/01 Mike Oliver
11/30/01 Old Man
11/30/01 Paul Lutus
11/30/01 Mike Oliver
11/30/01 David W. Cantrell
12/1/01 Paul Lutus
12/1/01 meron@cars3.uchicago.edu
12/1/01 Jim Bob
12/1/01 Paul Lutus
12/1/01 Jim Bob
12/1/01 Angus Rodgers
12/1/01 Mike Oliver
12/2/01 Angus Rodgers
12/1/01 meron@cars3.uchicago.edu
12/2/01 The Scarlet Manuka
12/4/01 Randy Poe
12/4/01 meron@cars3.uchicago.edu
12/1/01 Chan-Ho Suh
12/1/01 James Hunter
12/1/01 David W. Cantrell
12/2/01 Paul Lutus
12/2/01 David W. Cantrell
12/2/01 Paul Lutus
12/2/01 Angus Rodgers
12/2/01 Paul Lutus
12/2/01 Paul Lutus
12/2/01 Paul Lutus
12/3/01 Angus Rodgers
12/3/01 Paul Lutus
12/3/01 Angus Rodgers
12/3/01 Paul Lutus
12/3/01 meron@cars3.uchicago.edu
12/3/01 Chan-Ho Suh
12/3/01 Richard Herring
12/2/01 meron@cars3.uchicago.edu
12/3/01 Angus Rodgers
12/3/01 meron@cars3.uchicago.edu
12/3/01 Chan-Ho Suh
12/2/01 Paul Lutus
12/2/01 meron@cars3.uchicago.edu
12/2/01 David W. Cantrell
12/2/01 Paul Lutus
12/3/01 jmfbahciv@aol.com
12/2/01 The Scarlet Manuka
12/4/01 Randy Poe
12/2/01 Paul Lutus
12/2/01 Paul Lutus
12/2/01 The Scarlet Manuka
12/3/01 Paul Lutus
12/3/01 The Scarlet Manuka
12/3/01 Paul Lutus
12/3/01 The Scarlet Manuka
12/3/01 Paul Lutus
12/3/01 The Scarlet Manuka
12/3/01 Paul Lutus
12/3/01 Angus Rodgers
12/3/01 David W. Cantrell
12/3/01 Angus Rodgers
12/3/01 David W. Cantrell
12/3/01 Mike Oliver
12/3/01 The Scarlet Manuka
12/4/01 Angus Rodgers
12/3/01 Paul Lutus
12/3/01 The Scarlet Manuka
12/4/01 Paul Lutus
12/4/01 mareg@primrose.csv.warwick.ac.uk
12/4/01 The Scarlet Manuka
12/4/01 franz heymann
12/4/01 meron@cars3.uchicago.edu
12/7/01 Dustin Aleksiuk
12/7/01 David W. Cantrell
12/3/01 The Scarlet Manuka
12/3/01 David W. Cantrell
12/4/01 jmfbahciv@aol.com
12/3/01 Simon Nickerson
12/3/01 Jesse F. Hughes
12/3/01 Paul Lutus
12/3/01 Mike Oliver
12/3/01 Charles Dillingham
12/3/01 Paul Lutus
12/3/01 The Scarlet Manuka
12/3/01 meron@cars3.uchicago.edu
12/2/01 The Scarlet Manuka
12/3/01 Paul Lutus
12/3/01 The Scarlet Manuka
12/3/01 Paul Lutus
12/3/01 The Scarlet Manuka
12/3/01 Paul Lutus
12/3/01 Matt Gutting
12/3/01 The Scarlet Manuka
12/3/01 The Scarlet Manuka
12/3/01 Paul Lutus
12/3/01 The Scarlet Manuka
12/11/01