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

Warut, nice formula. For any n in Z+, here's an (2n-1)-times differentiable example that is not a rational function: H(x) = sgn(x) x^(2n). Which suggests a question: Question: --------- Does there exist a real analytic function f: R —> R that takes rationals to rationals, but is not a rational function? —Dan

On Feb 9, 2016, at 8:45 PM, Warut Roonguthai <warut822@gmail.com> wrote:

Here is my example of a continuous function which maps rationals to rationals, but is not a rational function:

F(x) = (-1)^floor(x) * frac(|x|) * (frac(|x|) - 1),

where frac(x) is the fractional part of x.