… is a continuous, increasing function on [0,1] with f(0)=0 and f(1)=1 that satisfies f'(x)=0 for all x in the open set [0,1]-C where, C⊂[0,1] is the Cantor Set.
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![f_0(x) := x \mbox{ for all } x \in [0,1]](http://chart.apis.google.com/chart?cht=tx&chf=bg,s,ffffff00&chco=000000ff&chs=25&chl=f_0%28x%29%20%3A%3D%20x%20%5Cmbox%7B%20for%20all%20%7D%20x%20%5Cin%20%5B0%2C1%5D)
…
is a continuous, increasing function on [0,1] with f(0)=0 and f(1)=1 that satisfies f'(x)=0 for all x in the open set [0,1]-C where, C⊂[0,1] is the Cantor Set.
