Science Fair Project Encyclopedia
The process begins by removing the middle 1/4 from the interval [0, 1] (the same as removing 1/8 on either side of the middle point at 1/2) so the remaining set is
The second step consists of removing the middle quarter of these two sets (the middle "quarters" now of size 1/64), and so on. More technically, this is done at each step by considering dyadic fractions of the form
contained in [0, 1] where a is an odd number. These fractions are then taken to be midpoints of the remaining subintervals, and
is then removed from either side of each of these midpoints (removing a total of around each such point).
It can also easily be shown to have a positive measure of 1/2 by observing that intervals of total length
are removed from [0, 1] during the construction.
The SVC is used in the construction of Volterra's function (see external link).
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