About the power of infinite sets
https://doi.org/10.26907/mrsej-24201
Abstract
Two main concepts of infinity (Aristotle's and Cantor's) are known in the history of mathematics. The last one, prevailing at present, was formulated by founder of the set theory Cantor about a century and a half ago. Cantor used (1) the diagonal method to compare the powers of the set of infinite rows of digits 0 and 1 and natural number series; (2) the Cantor's theorem about prevalence of the power of the set of all subsets of a set A over the power of A: |P(A)|>|A|. In this work it is shown by use of specific examples that Cantor's reasons can't be considered as strict proofs. Therefore, the concept of the common potential (Aristotelian) infinity seems to be more acceptable.
About the Author
L. K. Aminov
Academy of Sciences of the Republic of Tatarstan
Russian Federation
Russian Federation
Kazan 420013
References
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Review
For citations:
Aminov L.K. About the power of infinite sets. Magnetic Resonance in Solids. 2024;26(2):24201 (6 pp.). https://doi.org/10.26907/mrsej-24201
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