The “Cantor set” K is constructed by repeated replacement as follows. Start with the unit line-segment K0 = [0,1]. Form the first approximation 1 K by splitting 0 K into three equal subintervals and removing the first subinterval [0, ) 3 1 but leaving the other two. Repeat indefinitely, noting that the remaining pairs of subintervals at each stage should be treated separately.

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