Thank you for the reply! This is interesting, I didn't realize this. Unfortunately I'm still not sure I fully grasp it though: if I say 1.001 is "correctly roun

Thank you for the reply! This is interesting, I didn't realize this. Unfortunately I'm still not sure I fully grasp it though: if I say 1.001 is "correctly rounded", that is equivalent to saying it has error bounds of +/- 0.0005. I could say either of these and they would mean the same thing. So what does it mean when you say you an establish rigorous error bounds but you can't guarantee correct rounding? If you can decrease the error bounds (which it seems you can, given this is arbitrary-precision) then isn't that equivalent to being able to round with more digits (precision)?