## A Totally Ordered Set with Cardinality Strictly Between Natural and Real Numbers

**Authors:** Philip Druck

A totally ordered set is identified with cardinality strictly between natural (N) and real (R) numbers. This set, denoted DS, is essentially an experimental finding, identified in unrelated patented research on nonuniform data sampling and self-stabilizing computer arithmetic. Its theoretical validation here will provide concrete proof that the Continuum Hypothesis (CH) is false. Note that this is distinct from determining whether CH can or cannot be proven from current axioms of set theory, which is settled. Also note that the Generalized Continuum Hypothesis is not addressed. First, Cantor diagonalization is applied isomorphically to prove that DS has strictly more than Cardinality(N) points. Then three (3) distinct proofs are provided to show that DS contains strictly fewer than Cardinality(R) elements. Each proof relies on a distinct property of primes. It is surmised that the considerable research efforts to-date on CH missed this result due to over-generalization, by considering all Alephi sets, i=0.., ∞. Those efforts thereby missed the impact of primes specifically on Aleph0/Aleph1 sets.

**Comments:** 27 Pages.

**Download:** **PDF**

### Submission history

[v1] 2016-05-22 20:23:04

**Unique-IP document downloads:** 128 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.*

*
*