but it is odd how you get powers of pi as the infinite limits of Riemann summations... that only involve operations in each term in the sum involving conventional arithmetic on integers.. our decimal system is modular, trigonometric functions are periodic, and, as ive demonstrated, there exists a congruence between the the Kronecker delta or discrete Dirac whatever you know it as, and trigonometric sequences and series, however inversely to how pi occurs at the infinite limits of Riemann sums from purely integers, in the case of generating binary / integer sequences using trig functions it becomes requisite that 2*pi is a coefficient inside the arg of the trig function in order for the expression to be strictly defined on the integer number line