On 4/14/13 8:53 PM, Kim-Ee Yeoh wrote: > On Sun, Apr 14, 2013 at 3:28 PM, wren ng thornton <w...@freegeek.org> wrote: >> Whereas the problematic >> values due to infinities are overspecified, so no matter which answer you >> pick it's guaranteed to be the wrong answer half the time. >> >> Part of this whole problem comes from the fact that floats *do* decide to >> give a meaning to 1/0 (namely Infinity). > > I'm not sure what you mean about overspecification here, but in > setting 1/0 as +infinity (as opposed to -infinity), there's an easily > overlooked assumption that the limit is obtained "from above" as > opposed to "from below."

Setting 1/0 = +inf isn't the problem, or at least not the main one. Of course, there's always the question about which completion of the reals to use--- i.e., whether we have +inf vs -inf, or whether we just have a single point infinity. Rather, the NaN problem comes from trying to resolve things like: inf - inf inf * 0 inf / inf 0 / 0 The overspecification problem I mentioned is that each of these expressions has "too many" solutions. For example, we have the following equations: x * 0 == 0 -- where x is finite inf * y == inf * signum y -- where y /= 0 inf * 0 == ?? x - inf == -inf -- where x is finite inf - y == inf -- where y is finite inf - inf == ?? x / 0 == inf * signum x -- where x /= 0 0 / y == 0 -- where y /= 0 0 / 0 == ?? -- Live well, ~wren _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe