[Haskell-cafe] Re: 0/0 > 1 == False
Jonathan Cast
jonathanccast at fastmail.fm
Sat Jan 12 13:01:55 EST 2008
On 12 Jan 2008, at 1:45 AM, Achim Schneider wrote:
> Kalman Noel <kalman.noel at bluebottle.com> wrote:
>
>> Achim Schneider wrote:
>>> whereas lim( 0 ) * lim( inf ) is anything you want
>>
>> Indeed I suppose that »lim inf«, which is a notation I'm not familiar
>> with, is not actually defined to mean anything?
>>
> It's an ad-hoc expression of "as the slices approach zero size, their
> number approaches infinity". It's more an observation than anything
> else. I have no idea how a professional mathematician would formalise
> it.
I suspected as much.
You mean that, for any extended real number z, two sequences of real
numbers xn and yn may be chosen so that lim(xn) = 0, lim(yn) = inf,
and lim(xn * yn) = z.
jcc
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