Numeric comparison anomaly

[Gonçalo Rodrigues]

On Thu, 20 Feb 2003 22:58:15 -0700, Steven Taschuk
<staschuk at telusplanet.net> wrote:

>Quoth Erik Max Francis:
>  [...]
>> Infinity as a limit needs either to be positive infinity or negative
>> infinity; if unstated, it's positive infinity.  There's no "unsigned
>> infinity."
>
>There are uses for algebras on R U {oo}, that is, the real numbers
>augmented with a single unsigned infinity.  Gosper refers to such
>an algebra in his algorithms for continued fraction arithmetic,
>for example.
>

You can viw this as the circle S^1.

>If memory serves, the similar C U {oo}, i.e., the complex plane
>augmented with a single "point at infinity", finds use in complex
>analysis.  I think that set even has a name, but I'm damned if I
>can remember it.
>

It's the Riemman Sphere by golly. The infinity is the north pole. You
can also view it as the projective space of lines in R^2. Or...

>However, I don't know of a case in which having separate -oo, +oo
>and oo all at once is useful.  The closest thing I can think of is
>allowing the value 0/0 in rational arithmetic, but that's better
>conceived of as a NaN than as an infinity.

There are inumerous cases where adding a point of infinity is essential.
It is the simplest method of compactifying a space. And now that I am
studying Thom Spectra, it is also one of the essential tricks in the
Thom construction. The list goes on.

Uh..., wait... this is a Python newsgroup right? *crawls away*

With my best regards,
G. Rodrigues