Right, but then the domain isn't [0, 1] any more (it's got lots of double points, like 0.999… and 1, and 0.8999… and 0.9 etc.), and your function doesn't termin

Right, but then the domain isn't [0, 1] any more (it's got lots of double points, like 0.999… and 1, and 0.8999… and 0.9 etc.), and your function doesn't terminate on input 0.999…. I guess you meant to feed only the terminating decimal if there was one? Then, I agree, this is a good illustration of how a discontinuous function can violate all the nice properties on which the mathematics of functional programming relies.