The infinite set of real numbers R is not denumerable (that is, N_O < IRI). it suffices to show that the open interval (0,1) You may assume each real number can be written as an infinite decimal. If (0, 1) is  denumerable there is a bijection f: N* → (0, 1 ). Construct an infinite decimal (real  number) .a₁a₂· · · in {0,1) such that a_n is not the nth digit in the decimal expansion  of f(n). This number cannot be in Im f.]