Set Theory and Logic


The Function f(x) = C and the Continuum Hypothesis

Authors: Ron Ragusa

This paper examines whether or not an analysis of the behavior of the continuous function f(x) = C, where C is any constant, on the interval (a, b) where a and b are real numbers and a < b, will provide a method of proving the truth or falsity of the CH. The argument will be presented in three theorems and one corollary. The first theorem proves, by construction, the countability of the domain d of f(x) = C on the interval (a, b) where a and b are real numbers. The second theorem proves, by substitution, that the set of natural numbers N has the same cardinality as the subset of real numbers S on the given interval. The corollary extends the proof of theorem 2 to show that N and R are of the same cardinality. The third theorem proves, by logical inference, that the CH is true.

Comments: 5 Pages.

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Submission history

[v1] 2018-06-03 07:41:10
[v2] 2018-06-04 08:33:05

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