> if two of these are equal then in general you can't determine that they are in finite time. This is arguably a problem with floating point as well. Two compu

> if two of these are equal then in general you can't determine that they are in finite time. This is arguably a problem with floating point as well. Two computations F and G which ought to produce the same result can end up differing because of rounding errors. So equality testing is not advisable to do over floating point. Also, inequality of real numbers is still semi-decidable, which is useful. People keep bringing up these problems around not being able to compute discontinuous functions, but those problems still manifest themselves over the floating point numbers, in the sense that a small rounding error in the input can drastically affect the output. This obviously isn't a problem over the rational numbers, but a lot of operations like square-root are not possible over the rational numbers.