On Wed, 22 Jun 2016 16:30:49 +1000, Chris Angelico wrote:
> On Wed, Jun 22, 2016 at 4:17 PM, Steven D'Aprano
> <steve+comp.lang.pyt...@pearwood.info> wrote:
>> On Wednesday 22 June 2016 13:54, Dan Sommers wrote:
>>
>>> By the time Python returns a result for inf+3j, you're already in
>>> trouble (or perhaps Python is already in trouble).
>>
>> I don't see why. It is possible to do perfectly sensible arithmetic on INFs.
>
> Technically, arithmetic on INF is a short-hand for a limit. What is
> inf+1? Well, it's the limit of x+1 as x tends toward +∞, which is ∞.
> So inf+1 evaluates to inf.
>
>>>> inf = float("inf")
>>>> inf+1
> inf
>
> What's 5-inf? Same again - the limit of 5-x as x tends toward +∞.
> That's tending in the opposite direction, so we get infinity the other
> way:
>
>>>> 5-inf
> -inf
>
> So it's not really "doing arithmetic on infinity", as such. That said,
> I'm not entirely sure why "inf+3j" means we're already in trouble -
> Dan, can you elaborate? ISTM you should be able to do limit-based
> arithmetic, just the same.
What does (or can) inf+3j mean, and how can that be meaningfully
different from inf+4j, or 3+infj? My mental model for math's ℂ and
Python's complex() is the points on a plane plus a single infinity.¹
The quantity inf+3j is not a point on the plane, nor is it that single
infinity. To support inf+3j and 4+infj, Python's complex() would have
to be the points on a plane plus four "lines of infinity" plus something
to handle the intersections of the lines. Maybe it's me, but that model
creates more problems than it solves.
¹ Yes, I understand that math's ℂ and Python's complex() are different.
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