## The Real Numbers are Denumerable

**Authors:** James Edwin Rock

We show Cantor’s diagonal argument has an invalid premise. We create a non-hierarchical Level Set Theory by setting 1/(Aleph Null) = 0. The real numbers have the same cardinality as the set of natural numbers, since the power set of the natural numbers has the same cardinality as the natural numbers. Using binary decimals, we define r, 0 ≤ r ≤ 1 as the ratio of ones to the total number of digits for decimals in the closed interval [0, 1]. We use these ratios to show that the real numbers are denumerable.

**Comments:** 2 Pages.

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### Submission history

[v1] 2019-10-22 12:47:28

[v2] 2019-10-24 10:17:06

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