Prove that, for any natural number n, the graph of any increasing function f:[0,1]ā[0,1] can be covered by n rectangles each of area whose sides are parallel to the coordinate axes. Assume that a rectangle includes both its interior and boundary points.
(a) Assume that f(x) is continuous on [0,1].
(b) Do not assume that f(x) is continuous on [0,1]. (A Andjans, Riga)PS. (a) for O Level, (b) for A Level functiongraphRectanglescombinatoricscombinatorial geometrygeometryrectangle