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

 Messages: [ Previous | Next ]
 Paul Lutus Posts: 178 Registered: 12/7/04
Re: Paul Lutus says dumb things
Posted: Dec 2, 2001 1:31 PM

"David W. Cantrell" <DWCantrell@sigmaxi.org> wrote in message

> > I chose to express it as "as x approaches 0, 1/x approaches infinity."
>
> Chose (past tense)? If you had expressed it that way before, I would
> never have said "badly butchered". Your new statement makes good sense.

Again, thanks for your support, no irony intended. Many in this and a prior
thread have argued that a limit statement literally assigns the limit value
to the relevant variable, in other words, that a numeric variable x equals
infinity.

My previous post included the form I was arguing against, not the one I was
supporting. The clue is my use of "which, of course, is false ..." Here is
the original:

> > > "as x approaches the limit of zero, 1/x equals infinity"
> > >
> > > -- which, of course, is false and is not what a limit represents.

> > In either way of saying it, this is a special use of the equals sign,
> > with something other than the naive interpretation. My original point.

>
> But that original point is wrong. There is no "special use of the equals
> sign" in evidence. Limit_{x->0} 1/x = infinity is true in the projective
> extension, with "=" being used in the normal way.

But it doesn't mean that x equals infinity. That is a limit, not an
assignment. I know you may find this surprising, but that was the issue --
several people began arguing that x equaled infinity, and that therefore
infinity is a number in a default number system, one for which arithmetic
operations are defined in a conventional way.

It is like saying, "On Wednesday, we are in Cleveland." This does not say,
"We are in Cleveland." Same idea, and others have argued that the second
phrase summarizes the intention -- that x equals infinity, period.

The debate quickly wandered off to the issue of extended reals, a separate
topic, one hardly bearing on whether the original assertion is correct or
meaningful, in a number system in which arithmetic operations are defined in
a conventional way.

--
Paul Lutus
www.arachnoid.com

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