## 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.

**Download:** **PDF**

### 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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