Answering Hilbert's 1st Problem

TL;DR

This paper explores the foundational question of whether natural and real numbers are equivalent, presenting a construction that challenges Cantor's diagonal argument and discussing its philosophical implications.

Contribution

It introduces a novel construction claiming to establish equipollence of natural and real numbers, contradicting Cantor's diagonal argument and questioning established mathematical foundations.

Findings

Construction establishes equipollence in (0,1) interval

Contradicts Cantor's diagonal argument

Highlights philosophical implications of mathematical foundations

Abstract

Hilbert's first problem is of importance in relation to work being done in computational systems. It is the question of equipollence of natural and real numbers. By construction equipollence is established for real numbers in open interval (0, 1) and natural numbers and, from such to all real numbers. Construction stands in contradiction of the generally accepted diagonal argument of Cantor. Mathematics being irrefutable, in absence rejection of all theory of mathematics and logic, the problem exists in acceptance; that itself arises of more fundamental a problem in science generally. The problem within Hilbert's problem is of Schopenhauer's, et al, "will and representation" born.