Displaying similar documents to “Construction of normal numbers with respect to the Q-Cantor series expansion for certain Q”

Scientific intuition of Genii against mytho-‘logic’ of Cantor’s transfinite ‘paradise’

Alexander A. Zenkin (2005)

Philosophia Scientiae

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In the paper, a detailed analysis of some new logical aspects of Cantor’s diagonal proof of the uncountability of continuum is presented. For the first time, strict formal, axiomatic, and algorithmic definitions of the notions of potential and actual infinities are presented. It is shown that the actualization of infinite sets and sequences used in Cantor’s proof is a , but hidden, condition of the proof. The explication of the necessary condition and its factual usage within the framework...

On the structure of the intersection of two middle third Cantor sets.

Gregory J. Davis, Tian You Hu (1995)

Publicacions Matemàtiques

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Motivated by the study of planar homoclinic bifurcations, in this paper we describe how the intersection of two middle third Cantor sets changes as the sets are translated across each other. The resulting description shows that the intersection is never empty; in fact, the intersection can be either finite or infinite in size. We show that when the intersection is finite then the number of points in the intersection will be either 2 or 3 · 2. We also explore the Hausdorff dimension of...