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. On Tue, Feb 9, 2016 at 1:35 AM, Warren D Smith <warren.wds@gmail.com> wrote:
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)
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