For each complex parameter c, let fc:C→C be the quadratic polynomial defined by fc(z)=z2+c. A point z∈C is said to be part of an attracting cycle of period m of fc if m>0, fc[m](z)=z (where fc[m] denotes the m-fold iterate of fc), the iterate fc[m] is complex-differentiable at z, and the operator norm of its derivative at z satisfies ∥deriv(fc[m])(z)∥<1. The Mandelbrot set is the set of all parameters c∈C for which the orbit of 0 under fc does not escape to infinity, or equivalently, for which ∥fc[k](0)∥≤2 for all k≥0. Prove that the set of parameters c for which fc has an attracting cycle is dense in the Mandelbrot set.