Let f be the function of two variables defined in the following way: For x = .x1x2x3x4 … and y = .y1y2y3y4 … in the interval [0, 1) let f(x, y) = .z1z2z3z4 …,where zi =(xi − yi, ) mod 10 (i.e., zi is the remainder when xi + yi is divided by 10). For example, f(0.3258, 0.2564) = 0.5712.
(a) Show that f is discontinuous at (0.5, 0.5).
(b) Show that f is discontinuous at any point (x, y), where x and y are both nonzero and have terminating decimal expansions.
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