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Topic: Is zero an approximation?
Replies: 170   Last Post: Dec 8, 2001 12:57 AM

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 Paul Lutus Posts: 178 Registered: 12/7/04
Re: Is zero an approximation?
Posted: Nov 29, 2001 9:12 PM

"Mike Oliver" <oliver@math.ucla.edu> wrote in message
news://3C06E864.BF44CA7D@math.ucla.edu...
> Paul Lutus wrote:
>

> > Okay. How does this relate to the fact that infinity is not a number?
You
> > certainly cannot perform numerical operations on infinity.
>
> I certainly can, in some contexts, and it's a useful thing to do
> too.

Any context except a number system as that term is normally defined. See
below.

>
> For example, consider the one-point compactification of the complex
> plane, C u { oo }, where we topologize by saying the open sets are

generated
> by the open subsets of C, plus F u { oo } where F is any closed subset
> of C. We extend the arithmetic operations +,-,*,/ as follows:
>
> z+oo = oo+z = oo provided z != oo ( oo+oo is undefined)
> z-oo = oo-z = oo provided z != oo ( oo-oo is undefined)
> z*oo = oo*z = oo provided z != 0 ( 0*oo is undefined)
> z/oo = 0 provided z != oo ( oo/oo is undefined)
> oo/z = oo provided z != oo
> z/0 = oo provided z != 0 ( 0/0 is undefined)
>
> This is the "extended complex number system" or "complex sphere".
> It is the natural structure in which to study "Moebius transformations",
> which are functions z |-> (az+b)/(cz+d) for constant complex
> values a,b,c,d (a and b nonzero).

Meaningless rhetoric. The "extended complex number system" you describe
doesn't meet the definition of "number system," one property of which is the
exclusion of infinity.

Quote:

"No 'infinity' concept exists in the context of any number system, if by
number system one means a collection of concepts that have operations like
addition and multiplication the way familiar numbers do, operations which
obey the usual properties of arithmetic."

--
Paul Lutus
www.arachnoid.com

Date Subject Author
11/29/01 Jim Bob
11/29/01 Mike Oliver
11/29/01 Charles
11/29/01 Mike Oliver
11/30/01 Ken Oliver
12/1/01 David Libert
11/29/01 Paul Lutus
11/29/01 Jim Bob
11/29/01 Paul Lutus
11/29/01 Mike Oliver
11/29/01 Paul Lutus
11/29/01 Mike Oliver
11/29/01 Paul Lutus
11/29/01 Mike Oliver
11/29/01 Mike Oliver
11/29/01 Paul Lutus
11/29/01 Mike Oliver
11/29/01 Paul Lutus
11/29/01 Mike Oliver
11/30/01 Paul Lutus
11/30/01 Mike Oliver
11/30/01 Paul Lutus
11/30/01 David W. Cantrell
11/30/01 Mike Oliver
11/30/01 Paul Lutus
11/30/01 Mike Oliver
11/30/01 Paul Lutus
11/30/01 Jesse F. Hughes
11/30/01 Paul Lutus
11/30/01 Mike Oliver
11/30/01 Paul Lutus
11/30/01 Daryl McCullough
11/30/01 Mike Oliver
11/30/01 Jesse F. Hughes
11/30/01 The Scarlet Manuka
11/30/01 Paul Lutus
11/30/01 Matt Gutting
11/30/01 Paul Lutus
12/4/01 Matt Gutting
12/4/01 Paul Lutus
12/1/01 David W. Cantrell
12/1/01 Paul Lutus
12/1/01 Mike Oliver
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 The Scarlet Manuka
12/3/01 Mike Oliver
11/30/01 Paul Lutus
11/29/01 Mike Oliver
11/29/01 The Scarlet Manuka
11/30/01 Paul Lutus
11/30/01 Jim Bob
11/30/01 The Scarlet Manuka
11/30/01 Mike Oliver
11/30/01 The Scarlet Manuka
11/30/01 Paul Lutus
11/30/01 meron@cars3.uchicago.edu
11/29/01 James Hunter
11/30/01 neoprog
11/30/01 David W. Cantrell
12/1/01 David C. Ullrich
12/2/01 neoprog
12/3/01 David C. Ullrich
11/29/01 Paul Lutus
11/29/01 The Scarlet Manuka
11/30/01 Paul Lutus
11/30/01 The Scarlet Manuka
11/30/01 Paul Lutus
11/30/01 The Scarlet Manuka
11/30/01 Paul Lutus
11/30/01 The Scarlet Manuka
11/30/01 David W. Cantrell
11/30/01 mareg@primrose.csv.warwick.ac.uk
11/30/01 David W. Cantrell
11/30/01 Jon and Mary Frances Miller
11/30/01 Gregory L. Hansen
11/30/01 Doug Norris
11/30/01 James Hunter
11/30/01 Gregory L. Hansen
11/30/01 James Hunter
11/30/01 Virgil
11/30/01 Paul Lutus
11/30/01 James Hunter
11/30/01 Paul Lutus
11/30/01 James Hunter
11/30/01 Paul Lutus
11/30/01 mareg@primrose.csv.warwick.ac.uk
12/1/01 Jim Bob
12/2/01 Tubby Chubbs
12/2/01 Avoid normal situations.
11/30/01 neoprog
12/5/01 Randy Poe
11/30/01 Julian Fondren
12/2/01 The Scarlet Manuka
11/30/01 Julian Fondren
11/30/01 Paul Lutus
11/30/01 Jim Bob
11/30/01 Paul Lutus
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11/30/01 Paul Lutus
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12/1/01 Charles Dillingham
12/1/01 Mike Oliver
12/2/01 Charles Dillingham
12/2/01 Mike Oliver
12/2/01 Mike Oliver
12/2/01 Mike Oliver
12/2/01 Bob Kolker
12/2/01 Mike Oliver
12/2/01 Bob Kolker
12/2/01 Mike Oliver
12/2/01 Bob Kolker
12/2/01 Mike Oliver
12/3/01 David W. Cantrell
12/3/01 Bob Kolker
12/3/01 The Scarlet Manuka
12/3/01 Bob Kolker
12/3/01 The Scarlet Manuka
12/3/01 meron@cars3.uchicago.edu
12/2/01 Bob Kolker
12/2/01 Mike Oliver
12/3/01 Bob Kolker
12/3/01 The Scarlet Manuka
12/3/01 Mike Oliver
12/5/01 Mike Oliver
12/7/01 David W. Cantrell
12/8/01 Mike Oliver
12/3/01 Charles Dillingham
12/3/01 Mike Oliver
12/5/01 Charles Dillingham
12/5/01 Mike Oliver
12/5/01 Mike Oliver
11/29/01 Bryan Reed
11/30/01 Jim Bob
11/30/01 Paul Lutus
11/29/01 Uncle Al
11/29/01 Stephen Norris
12/2/01 James Hunter
11/30/01 glenn
11/30/01 James Hunter
11/30/01 Rushtown
11/30/01 Jesse F. Hughes
11/30/01 Virgil
11/30/01 Bob Kolker
11/30/01 Julian Fondren
11/30/01 Paul Cardinale
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11/30/01 franz heymann
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12/3/01 Paul Cardinale
12/3/01 Paul Lutus
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12/7/01 Paul Lutus
11/30/01 Stephen Norris
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12/1/01 mensanator
12/3/01 Juuichirou Tendou
12/6/01 Keith Ramsay