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Re: Infinity + Infinity (or NegInfinity - NegInfinity)

From Kaba <kaba@nowhere.com>
Newsgroups alt.comp.lang.borland-delphi, alt.math, comp.arch, comp.graphics.algorithms, comp.lang.c
Subject Re: Infinity + Infinity (or NegInfinity - NegInfinity)
Date 2011-10-08 17:43 +0300
Message-ID <MPG.28fa8e225336ca499899d3@news.cc.tut.fi> (permalink)
References <89f27$4e8f9f40$5419acc3$12829@cache4.tilbu1.nb.home.nl>

Cross-posted to 5 groups.

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Skybuck Flying wrote:
> Hello,
> 
> I was just wondering what happens if "Infinity" is added to "Infinity" when 
> it comes to floating point numbers ?
> 
> And also what happens if "Negative Infinity" is added to "Negative 
> Infinity"... ?
> 
> In Delphi these are defined as follows (in the math.pas unit):
> 
> const
>   Infinity    =  1.0 / 0.0;
>   NegInfinity = -1.0 / 0.0;
> 
> As far as I know this conforms to some kind of floating point standard.

Here are some interesting properties of the IEEE floating point 
standard, which is the underlying technology behind most home computers. 
The behaviour of high-level programming languages tend to mirror it 
closely. Let x be some positive, regular, floating point number. The 
basic mathematical model is the affinely extended reals, but the 
standard defines a bit more (see division by zero).

Zeros:

* There are two zeros, +0 and -0.
* -0 = -(+0)
* Floating point comparison is defined so that +0 = -0 is true.

Not-A-Number (NaN):

* Produced as an error value, for example with +0 / +0.
* Multiplying, adding, subtracting or dividing with a NaN produces a 
NaN. The NaN is said to be propagated.
* All comparisons (<, >, =, !=, <=, >=) with a NaN yield false.

Infinities:

* There is infinity (oo) and minus infinity (-oo). 
* -oo = -(oo)
* oo + oo = oo
* -oo + -oo = -oo
* oo + -oo = NaN
* +-x + oo = oo
* +-x + -oo = -oo
* Subtraction similarly...

Division by zero:

* +-x / +0 = +-oo
* +-x / -0 = -+oo
* +-0 / +-0 = NaN

Multiplication by infinities:

* +-x * oo = +-oo
* +-x * -oo = -+oo
* +0 * +-oo = +-0
* -0 * +-oo = -+0

Division by infinities:

* +-x / oo = +-0
* +-x / -oo = -+0

-- 
http://kaba.hilvi.org

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Infinity + Infinity (or NegInfinity - NegInfinity) "Skybuck Flying" <Windows7IsOK@DreamPC2006.com> - 2011-10-08 02:54 +0200
  Re: Infinity + Infinity (or NegInfinity - NegInfinity) Robert Myers <rbmyersusa@gmail.com> - 2011-10-07 18:40 -0700
    Re: Infinity + Infinity (or NegInfinity - NegInfinity) James Kuyper <jameskuyper@verizon.net> - 2011-10-07 22:39 -0400
  Re: Infinity + Infinity (or NegInfinity - NegInfinity) William Elliot <marsh@rdrop.com> - 2011-10-07 19:56 -0700
    Re: Infinity + Infinity (or NegInfinity - NegInfinity) Jasen Betts <jasen@xnet.co.nz> - 2011-10-08 06:45 +0000
      Re: Infinity + Infinity (or NegInfinity - NegInfinity) gordonb.eug6r@burditt.org (Gordon Burditt) - 2011-10-08 02:37 -0500
        Re: Infinity + Infinity (or NegInfinity - NegInfinity) William Elliot <marsh@rdrop.com> - 2011-10-08 21:40 -0700
          Re: Infinity + Infinity (or NegInfinity - NegInfinity) Kaba <kaba@nowhere.com> - 2011-10-09 12:17 +0300
  Re: Infinity + Infinity (or NegInfinity - NegInfinity) Jasen Betts <jasen@xnet.co.nz> - 2011-10-08 06:33 +0000
  Re: Infinity + Infinity (or NegInfinity - NegInfinity) "Skybuck Flying" <Windows7IsOK@DreamPC2006.com> - 2011-10-08 16:41 +0200
    Re: Infinity + Infinity (or NegInfinity - NegInfinity) kenney@cix.compulink.co.uk - 2011-10-09 04:01 -0500
  Re: Infinity + Infinity (or NegInfinity - NegInfinity) Kaba <kaba@nowhere.com> - 2011-10-08 17:43 +0300
    Re: Infinity + Infinity (or NegInfinity - NegInfinity) "christian.bau" <christian.bau@cbau.wanadoo.co.uk> - 2011-10-08 10:20 -0700
      Re: Infinity + Infinity (or NegInfinity - NegInfinity) Kaba <kaba@nowhere.com> - 2011-10-08 22:35 +0300
    Re: Infinity + Infinity (or NegInfinity - NegInfinity) nmm1@cam.ac.uk - 2011-10-08 18:55 +0100
      Re: Infinity + Infinity (or NegInfinity - NegInfinity) Kaba <kaba@nowhere.com> - 2011-10-08 23:03 +0300
        Re: Infinity + Infinity (or NegInfinity - NegInfinity) nmm1@cam.ac.uk - 2011-10-08 21:27 +0100
          Re: Infinity + Infinity (or NegInfinity - NegInfinity) James Kuyper <jameskuyper@verizon.net> - 2011-10-08 17:28 -0400
            Re: Infinity + Infinity (or NegInfinity - NegInfinity) Robert Myers <rbmyersusa@gmail.com> - 2011-10-08 18:15 -0400
            Re: Infinity + Infinity (or NegInfinity - NegInfinity) nmm1@cam.ac.uk - 2011-10-08 23:23 +0100
              Re: Infinity + Infinity (or NegInfinity - NegInfinity) James Kuyper <jameskuyper@verizon.net> - 2011-10-08 21:29 -0400
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) nmm1@cam.ac.uk - 2011-10-09 10:01 +0100
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) Al Grant <algrant@myrealbox.com> - 2011-10-12 06:14 -0700
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) nmm1@cam.ac.uk - 2011-10-12 15:25 +0100
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) James Kuyper <jameskuyper@verizon.net> - 2011-10-12 12:10 -0400
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) nmm1@cam.ac.uk - 2011-10-12 18:41 +0100
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) James Kuyper <jameskuyper@verizon.net> - 2011-10-12 15:32 -0400
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) nmm1@cam.ac.uk - 2011-10-12 20:44 +0100
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) Robert Myers <rbmyersusa@gmail.com> - 2011-10-12 18:11 -0700
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) Andrew Reilly <areilly---@bigpond.net.au> - 2011-10-13 03:48 +0000
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) "Paul A. Clayton" <paaronclayton@gmail.com> - 2011-10-12 23:15 -0700
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) Terje Mathisen <"terje.mathisen at tmsw.no"> - 2011-10-13 09:12 +0200
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) "Paul A. Clayton" <paaronclayton@gmail.com> - 2011-10-13 00:49 -0700
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) Terje Mathisen <"terje.mathisen at tmsw.no"> - 2011-10-13 10:37 +0200
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) EricP <ThatWouldBeTelling@thevillage.com> - 2011-10-13 11:04 -0400
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) EricP <ThatWouldBeTelling@thevillage.com> - 2011-10-13 17:15 -0400
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) Terje Mathisen <"terje.mathisen at tmsw.no"> - 2011-10-14 09:22 +0200
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) EricP <ThatWouldBeTelling@thevillage.com> - 2011-10-14 13:37 -0400
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) "Andy \"Krazy\" Glew" <andy@SPAM.comp-arch.net> - 2011-10-13 11:11 -0700
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) Al Grant <algrant@myrealbox.com> - 2011-10-14 01:04 -0700
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) nmm1@cam.ac.uk - 2011-10-13 09:07 +0100
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) Al Grant <algrant@myrealbox.com> - 2011-10-13 07:00 -0700
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) Robert Myers <rbmyersusa@gmail.com> - 2011-10-14 10:54 -0700
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) Andrew Reilly <areilly---@bigpond.net.au> - 2011-10-14 22:36 +0000
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) Terje Mathisen <"terje.mathisen at tmsw.no"> - 2011-10-15 09:26 +0200
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) "Paul A. Clayton" <paaronclayton@gmail.com> - 2011-10-15 05:39 -0700
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) Terje Mathisen <"terje.mathisen at tmsw.no"> - 2011-10-15 14:56 +0200
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) nmm1@cam.ac.uk - 2011-10-17 08:37 +0100
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) Terje Mathisen <"terje.mathisen at tmsw.no"> - 2011-10-17 12:03 +0200
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) nmm1@cam.ac.uk - 2011-10-17 11:13 +0100
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) Terje Mathisen <"terje.mathisen at tmsw.no"> - 2011-10-17 22:30 +0200
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) "Paul A. Clayton" <paaronclayton@gmail.com> - 2011-10-17 14:47 -0700
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) Terje Mathisen <"terje.mathisen at tmsw.no"> - 2011-10-18 11:33 +0200
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) nmm1@cam.ac.uk - 2011-10-18 10:21 +0100
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) nmm1@cam.ac.uk - 2011-10-18 08:16 +0100
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) Terje Mathisen <"terje.mathisen at tmsw.no"> - 2011-10-18 14:26 +0200
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) nmm1@cam.ac.uk - 2011-10-18 13:32 +0100
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) Terje Mathisen <"terje.mathisen at tmsw.no"> - 2011-10-18 17:47 +0200
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) nmm1@cam.ac.uk - 2011-10-18 17:51 +0100
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) Terje Mathisen <"terje.mathisen at tmsw.no"> - 2011-10-19 10:37 +0200
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) nmm1@cam.ac.uk - 2011-10-19 09:36 +0100
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) Terje Mathisen <"terje.mathisen at tmsw.no"> - 2011-10-19 11:46 +0200
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) nmm1@cam.ac.uk - 2011-10-19 10:45 +0100
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) Terje Mathisen <"terje.mathisen at tmsw.no"> - 2011-10-19 13:11 +0200
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) nmm1@cam.ac.uk - 2011-10-19 12:12 +0100
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) Terje Mathisen <"terje.mathisen at tmsw.no"> - 2011-10-19 16:22 +0200
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) nmm1@cam.ac.uk - 2011-10-19 15:16 +0100
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) Andrew Reilly <areilly---@bigpond.net.au> - 2011-10-15 20:16 +0000
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) Robert Myers <rbmyersusa@gmail.com> - 2011-10-15 16:26 -0700
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) Terje Mathisen <"terje.mathisen at tmsw.no"> - 2011-10-17 08:14 +0200
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) nmm1@cam.ac.uk - 2011-10-17 08:22 +0100
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) Terje Mathisen <"terje.mathisen at tmsw.no"> - 2011-10-17 11:39 +0200
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) rpw3@rpw3.org (Rob Warnock) - 2011-10-17 21:00 -0500
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) "Skybuck Flying" <Windows7IsOK@DreamPC2006.com> - 2011-10-18 05:44 +0200
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) "Andy \"Krazy\" Glew" <andy@SPAM.comp-arch.net> - 2011-10-17 21:35 -0700
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) Jasen Betts <jasen@xnet.co.nz> - 2011-10-24 02:40 +0000
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) Phil Carmody <thefatphil_demunged@yahoo.co.uk> - 2011-10-27 00:32 +0300
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) Terje Mathisen <"terje.mathisen at tmsw.no"> - 2011-10-27 10:41 +0200
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) Phil Carmody <thefatphil_demunged@yahoo.co.uk> - 2011-10-27 13:10 +0300
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) Terje Mathisen <"terje.mathisen at tmsw.no"> - 2011-10-27 13:53 +0200
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) Keith Thompson <kst-u@mib.org> - 2011-10-12 12:34 -0700
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) Al Grant <algrant@myrealbox.com> - 2011-10-13 06:39 -0700
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) James Kuyper <jameskuyper@verizon.net> - 2011-10-13 10:34 -0400
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) Al Grant <algrant@myrealbox.com> - 2011-10-14 00:54 -0700
            Re: Infinity + Infinity (or NegInfinity - NegInfinity) Larry Hewitt <larryhwtt@comporium.net> - 2011-10-09 21:35 -0400
              Re: Infinity + Infinity (or NegInfinity - NegInfinity) "Skybuck Flying" <Windows7IsOK@DreamPC2006.com> - 2011-10-10 04:37 +0200
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) Larry Hewitt <larryhwtt@comporium.net> - 2011-10-10 13:58 -0400
                Re: Infinity + Infinity (or NegInfinity - NegInfinity) "Skybuck Flying" <Windows7IsOK@DreamPC2006.com> - 2011-10-13 20:17 +0200
        Re: Infinity + Infinity (or NegInfinity - NegInfinity) Arivald <arivald_@AT_interia_DOT_.pl> - 2011-10-13 12:10 +0200

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