## The Real Numbers are Denumerable in Level Set Theory

**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. We prove that the real numbers have the same cardinality as the set of natural numbers, by showing that the power set of the natural numbers has the same cardinality as the natural numbers. This shows there is a one to one mapping from the set of natural numbers to the real numbers, making the real numbers a denumerable set.

**Comments:** 1 Page. This paper contains the simplest possible mapping of the set of natural numbers to the real numbers.

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### Submission history

[v1] 2019-07-27 10:07:01

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