Cantorternary Set

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Cantorternary Set

a perfect set of points on a line that does not contain a single interval; it was constructed by G. Cantor in 1883. It is obtained by first removing the middle third (1/3, 2/3) from the closed interval [0, 1], then removing the middle thirds (1/9, 2/9) and (7/9, 8/9) of the remaining closed intervals[0, 1/3] and [2/3, 1], and so on. The Cantor ternary set has the power of the continuum. The set may be defined arithmetically as the totality of ternary fractions 0. a₁ … a_n …, where each of the digits a, ₁a₂, …, a_n, … is 0 or 2. The Cantor ternary set plays an important role in various problems of mathematics (in topology and in the theory of functions of a real variable).

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