[Python-Dev] PEP239 (Rational Numbers) Reference Implementation and new issues

[Erik Max Francis]

Greg Ewing wrote:

> My own faded memory says: L'Hopital's Rule. Differentiate top
> and bottom and take the limit of that instead. Repeat until
> top and bottom don't both go to 0.

This also works for other indeterminate limits, e.g., oo/oo.  However
there's an important distinction here that's being left out.  Infinity
and indeterminacy, strictly speaking, only apply when _limits_ are being
taken.  If there's no limit that you're taking that gives you 1/0 when
naively substituted, then you're not talking about something that's
"infinite" or "indeterminate," you're talking about something that's
simply undefined.

> There's no doubt some terribly good reason why this works,
> 
> but I can't remember it, if I ever knew...

Well, L'Hopital's rule has a proof associated with it.  Either you can
follow the proof to enlightenment or just trust in the fact that it
really does work.

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