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.
Unique-IP document downloads: 28 times
Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.
Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.