Guys please help me solve this problem(it is troubling me).......
Let f:R+ --> R be defined as f(x)=x + (1/x) -\(\lfloor\) x + (1/x) \(\rfloor\). It is required to prove that there are infintely many rational numbers u so that
\(\bullet\, 0<u<1, \)
\(\bullet\, u,\,f(u),\, f(f(u)) \:are\: all\: distinct,\: and \)
\(\bullet\, f(f(u))= \,f(f(f(u))) \)