/sci/ - Science & Math

Any reason I can't just use
[eqn]f(y) = \frac{d(x,y)}{1 + d(x,y)}[/eqn]
?


I guess the hint wants me to construct functions [math]f_k[/math] with [math]f_k(x) = 0[/math] and [math]f_k(y) = 1[/math] for [math]y \in F_k[/math] and then consider
[eqn]f(y) = \sum_{k=1}^\infty \frac{f_k(y)}{2^k}[/eqn]
but is this really needed?