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 string conditioning, a technique that limits the range of a string over portions of its sub-domain 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.