Let f : 10 , 1 1 0 , 1 1 be a ( weakly ) increasing function . Prove that a = infit E O , 1 : f t ) lt; t exists and is fixed by f .

Please help me prove the following question about fixed points of a function.

1 . Let f : 10 , 1 1 0 , 1 1 be a ( weakly ) increasing function . Prove thata = infit E O , 1 : f t ) < texists and is fixed by f . Show further that a is the smallest fixed point of f