Numeric comparison anomaly

Steven Taschuk staschuk at
Fri Feb 21 06:58:15 CET 2003

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.

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.

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.

Steven Taschuk                            staschuk at
Every public frenzy produces legislation purporting to address it.
                                           (Kinsley's Law)

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