A Possible Resolution to Hilbert’s first Problem by Applying Cantor’s Diagonal Argument with Conditioned Subsets of R, With That of (N,R)

Abstract

We present herein a new approach to the Continuum hypothesis CH. We will employ a string conditioning, a technique that limits the range of a string over some of its sub-domains for forming subsets K of R. We will prove that these are well defined and in fact proper subsets of R by making use of Cantor’s Diagonal argument in its original form to establish the cardinality of K between that of (N,R) respectively