Re: [math-fun] Can a nonconstant continuous function on the reals

Question: Can a nonconstant continuous function on the reals assume only rational values? Answer: No, because of https://en.wikipedia.org/wiki/Intermediate_value_theorem More interesting question: Find a function F(x), which is continuous (the smoother the better) which maps rationals to rationals, but is not a rational function. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)