**Category:**

Research Papers

**Sub-Category:**

Mathematics and Applied Mathematics

**Date Published:**

February 19, 2021

**Keywords:**

rational numbers, dense order, ω-order, recursive definitions

**Abstract:**

This chapter proves an inconsistency in the set of the rational numbers as a consequence of the fact that, being densely ordered, the rational numbers can also be reordered by means of any bijection with the set of the natural numbers so that between any two successive rational numbers no other rational number does exist.

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