Set Theory and Logic


Interval Sieve Algorithm - Creating a Countable Set of Real Numbers from a Closed Interval

Authors: Ron Ragusa

The Interval Sieve Algorithm is a method for generating a list of real numbers on any closed interval [ri, rj] where ri < rj, which can then be defined as the domain of the function f(x) = C. The purpose of this paper is to delineate the steps of the algorithm and show how it will generate a countable list from which the domain for the function f(x) = C can be defined. Having constructed the list we will prove that the list is complete, that it contains all the numbers in the interval [ri, rj]. Lastly we will demonstrate a restricted proof of the Continuum Hypothesis.

Comments: 6 Pages.

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Submission history

[v1] 2019-03-03 15:04:19
[v2] 2019-03-05 22:33:09
[v3] 2019-03-06 16:13:39
[v4] 2019-03-08 06:41:25

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