## Showing the Real Numbers are Denumerable Using Binary Digit Ratios

**Authors:** James Edwin Rock

Cantor’s diagonal argument starts with an invalid premise. 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. Since the reals numbers have the same cardinality as the power set of the natural numbers, there is no hierarchy of infinities in Level Set Theory.

**Comments:** 2 Pages.

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### Submission history

[v1] 2019-09-13 08:42:33

[v2] 2019-09-17 07:00:17

[v3] 2019-09-25 09:24:40

[v4] 2019-09-27 12:32:40

[v5] 2019-10-07 09:37:21

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