Welcome to Dirichlet Bird! This fun game is designed to teach and educate people on the Dirichlet function. In mathematics, the Dirichlet function is the indicator function of the set of rational numbers, for more information about the Dirichlet function read below. Information ------------------------------------------------------------------------- The Dirichlet function is a piecewise function f(x) when if x is a rational number f(x) = 1 and if x is an irrational number f(x) = 0. Because of the nature of rational and irrational numbers (specifically the fact that in between any two rational numbers, there is an irrational number), this function is not continuous on any interval. Anytime that you try and look at just an interval of this function you still wind up with at least one irrational number and two rational numbers or vice versa. Because of this, the function is not continuous at any point. It is an indicator function which means that it sets all of a certain type of number (rationals) to 1 and all other values (irrational) to zero. Due to its continuity issues, this function is not Riemann summable. Johann Peter Gustav Lejeune Dirichlet presented this function in 1829. He was a German mathematician. He was on February 13, 1805, and died on May 5, 1859. Dirichlet created this function to readjust the way that we think about functions. It was designed to be a function that was discontinuous at all points. He was trying to find a piecewise function that the Fourier series wouldn’t exist.
