Re: [Haskell-cafe] Re: 0/0 > 1 == False

On Sat, 12 Jan 2008, Achim Schneider wrote:

Kalman Noel wrote:

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Achim Schneider wrote:

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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.

In Haskell you could professionally formalize it, if you would have a function, which computes the limit of a sequence: limit :: [Real] -> Real (Cf. "Why functional progrmaming matters" http://www.math.chalmers.se/~rjmh/Papers/whyfp.html) let xs = iterate (1+) 1 -- example for "lim (inf)" ys = map recip xs -- example for "lim (0)" in limit (zipWith (*) xs ys) If 'limit xs' and 'limit ys' are defined, then it holds limit (zipWith (*) xs ys) == limit xs * limit ys but in your case 'limit xs' does not exist. You can imagine it as infinity, but to make it formally safe, you need something non-standard analysis.