Let f:[a,b]→[a,b] be a continuous function and let p∈[a,b]. Define p0=p and pn+1=f(pn) for n=0,1,2,.... Suppose that the set Tp={pn:n=0,1,2,...} is closed, i.e., if x∈Tp then ∃δ>0 such that for all x′∈Tp we have ∣x′−x∣≥δ.
Show that Tp has finitely many elements. functionreal analysisreal analysis solved