Problem
ALG-B3-M08-P001 Forbidden Fixed Point
#1
★★☆☆☆ Level 2 of 5
Let \(f(f(x))=x+1\) for all \(x\). Prove that there is no \(a\) such that \(f(a)=a\).
Substitute a fixed point into the iteration.
If \(f(a)=a\), then \(f(f(a))=f(a)=a\). But by the condition, \(f(f(a))=a+1\). This gives the contradiction \(a=a+1\).
Basic fixed point obstruction.