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> From: Aubrey Jaffer <agj@xxxxxxxxxxxx> > Inverting +/0. or -/0. returns 0.0. So the name "error object" > wouldn't seem to apply either. - I still don't understand how it's acceptable for (/ 1/-0.0) => 0.0, as it seems neither necessary, nor desirable to propagate IEEE-754 mistake. > | This brings up an important distinction in "infinities;" > | When you divide by exact zero you get an absolute infinity. > | (which, perversely, is neither positive nor negative, because > | exact zero isn't positive or negative.) Call this EO1. > > We have already covered this ground. Division by zero is undefined; > SRFI-70 extends division by returning infinities in these cases: > (/ -5. 0) ==> -/0.; (/ 1. 0) ==> +/0., which are consistent with > the one-sided limits: > > (limit / 0 1.0e-9) ==> +/0. > (limit / 0 -1.0e-9) ==> -/0. - however as multiplication by 0 should result in 0, 0/x => 0 regardless of its denominator. > | When you divide 1 by (say) 5e-323, you get a different kind of > | EO, which is "results too large to represent" but which > | is often mistaken for an actual infinity. Call this EO2. > > The result of division by zero was chosen to be the same as the result > of (/ 1 5e-323). We could split +/0 into any number of regions. One > was chosen, which happens to be supported by IEEE-754. - who's model of infinitesimals isn't likely something worthy of mimicking.