Re: Computer arithmetic problems worth exploring

Message-ID	<4DCCA207.6030403@SPAM.comp-arch.net> (permalink)
Date	2011-05-12 20:14 -0700
From	"Andy \"Krazy\" Glew" <andy@SPAM.comp-arch.net>
Organization	comp-arch.net
Newsgroups	comp.arch
Subject	Re: Computer arithmetic problems worth exploring
References	<0fbd4179-1128-4ae0-94cf-91fcc25f6401@glegroupsg2000goo.googlegroups.com> <iqderu$k1$1@gosset.csi.cam.ac.uk> <4DCAED84.8000007@SPAM.comp-arch.net> <iqf4rr$bjr$1@gosset.csi.cam.ac.uk>

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On 5/11/2011 4:07 PM, nmm1@cam.ac.uk wrote:
> In article<4DCAED84.8000007@SPAM.comp-arch.net>,
> Andy \"Krazy\" Glew<andy@SPAM.comp-arch.net>  wrote:
>>
>> While we are at it, I have been thinking about complex numbers more and
>> more.  What are the infinitesimals for complex numbers?  Intervals for
>> the angle, and/or -0,0,+0, -inf,inf,+inf for the radius?
>
> There's only one.  The consistent compactification of the real
> line has two infinities, one at each end.  That of the complex
> numbers is the Riemann sphere, with a single point at infinity.
>
> You will immediately notice that using Cartesian representation
> with two compactified real numbers does not map well onto what
> is needed for complex ones.  It's a devil of a problem, technically
> most easily addressed by using polar coordinates.  However, that
> is a step too far for most people ....


Sorry the Riemann sphere formulation for complex is equivalent to the 
affine for reals, with only a single infinity in both cases.

As you may have noticed, I immediately jump to polar coordinates for 
directed infinities.

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Re: Computer arithmetic problems worth exploring "Paul A. Clayton" <paaronclayton@gmail.com> - 2011-05-10 19:24 -0700
  Re: Computer arithmetic problems worth exploring nmm1@cam.ac.uk - 2011-05-11 08:46 +0100
    Re: Computer arithmetic problems worth exploring "Andy \"Krazy\" Glew" <andy@SPAM.comp-arch.net> - 2011-05-11 13:11 -0700
      Re: Computer arithmetic problems worth exploring nmm1@cam.ac.uk - 2011-05-11 21:51 +0100
        Re: Computer arithmetic problems worth exploring "Andy \"Krazy\" Glew" <andy@SPAM.comp-arch.net> - 2011-05-12 20:12 -0700
          Re: Computer arithmetic problems worth exploring Quadibloc <jsavard@ecn.ab.ca> - 2011-05-12 20:53 -0700
          Re: Computer arithmetic problems worth exploring Jason Riedy <jason@lovesgoodfood.com> - 2011-05-13 00:03 -0400
      Re: Computer arithmetic problems worth exploring nmm1@cam.ac.uk - 2011-05-12 00:07 +0100
        Re: Computer arithmetic problems worth exploring "Andy \"Krazy\" Glew" <andy@SPAM.comp-arch.net> - 2011-05-12 20:14 -0700

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