On the Transcendency of Non-constant Periodic Functions

Two theorems: I. if y=f(x) is transcendental, so does its inverse; and II. any periodic function, not being a constant, is transcendental, are proved. By means of them, the transcendency of the circular function, exponential function and their inverses are established. Apart from these, such functions as Dirichlet function and kronecker delta symbol are pointed out to be transcendental.