Cantor ternary set

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Cantor ternary set

[′kän·tȯr ′tər·nə·rē ‚set]
(mathematics)
A perfect, uncountable, totally disconnected subset of the real numbers having Lebesgue measure zero; it consists of all numbers between 0 and 1 (inclusive) with ternary representations containing no ones.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
This math text explains the origins and underlying assumptions of the Cantor set, an ordered abelian group.
Let C be a copy of the Cantor set in the interval [-1, 1].
Yet he seems to have been derailed by his offhand remark to a reporter that Eric Cantor set off his "gaydar."
where F is a Cantor set, [H.sub.[alpha]](x) is the a dimensional Hausdorff measure, [sub.0] [I.sup.([alpha]).sub.x] (x) is the local fractional integral operator [24-30], and [GAMMA](x) is the Gamma function.
This function, related to the standard Cantor set, finds applications in areas like wave-particle interactions [2], crystal growth [3], and mode locking of the 3D coherent states in high-Q laser cavities [4].
To realize this fact, we attempt to check the case of the Cantor set; see Figure 1 [8, 9].
Stewart also mentions the amazing, monstrous Cantor set, which is made by taking an interval and deleting the middle third, then deleting the middle third of the two remaining intervals, and so on, for ever.
It is generally accepted that the (presumably) non-contradictory Zermelo-Fraenkel set theory ZF with the axiom of choice is the most accurate and complete axiomatic representation of the core of Cantor set theory.
For every r [member of] (0, 1/2) the ICBM [[micro].sub.r] is singular and its spectrum is a Cantor set. For r = 1/2 we get Lebesgue distribution and Legendre polynomials.
Set A is the classical Cantor set less the number one and the left end points of the open intervals removed from [0,1] to form the Cantor set.
This configuration satisfies the first step of the classical triadic fractal Cantor set. Other first-step dividing methods also can be performed.