It is not very important, but I am asked to prove that the periodic points in the tent map are dense on the closed interval $[0,1]$.
Anyway, I can prove that there are an infinite number of periodic points on that interval (and they are unique). Does that directly imply that therefore those points are dense?
I know that all the periodic points are the rationals in this case, and it is enough to say that the rationals are dense, but I was looking at different proofs that all the periodic points of the tent map are rationals, and they seem way beyond this course.
So, regardless, my question about infinitely many unique points implying density (on a closed interval) still stands. Thank you!