Re: [Haskell-cafe] NaN as Integer value

On 4/14/13 8:53 PM, Kim-Ee Yeoh wrote:

On Sun, Apr 14, 2013 at 3:28 PM, wren ng thornton wrote:

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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