Set Theory and Logic


Mapping the Real Numbers to the Set of Natural Numbers

Authors: James Edwin Rock

The terminating decimal fractions in the open interval (0, 1) are put in one to one correspondence with the set of positive integers. This shows that attempting to map the set of real numbers to the natural numbers by listing them as infinite decimal fractions is futile. The real numbers are represented as the limit of partial decimal sums. We show how the real numbers can be represented as a denumerable set. We create a new (Level Set Theory). The set of real numbers has the same cardinality as the set of natural numbers.

Comments: 1 Page. Paper contains an explicit mapping of the real numbers to the natural numbers.

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Submission history

[v1] 2019-06-10 07:28:42
[v2] 2019-06-19 07:09:49 (removed)
[v3] 2019-06-22 16:58:56

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