Achim Schneider <[EMAIL PROTECTED]> wrote: > Kalman Noel <[EMAIL PROTECTED]> 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. > Actually, lim( 0 ) * lim( inf ) isn't anything but equals one, and the anything is defined to one (or, rather, is _one_ anything) to be able to use the abstraction. It's a bit like the difference between eight pens and a box of pens. If someone knows how to properly formalise n = 1, please speak up.
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