1986/03/01 by Chris Freiling · 6 citations
Mathematics · Computer Science · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #Mathematical and Theoretical Analysis
paper · doi:10.2307/2273955
openalex publication_date 1986/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
Abstract We will give a simple philosophical “proof” of the negation of Cantor's continuum hypothesis (CH). (A formal proof for or against CH from the axioms of ZFC is impossible; see Cohen [1].) We will assume the axioms of ZFC together with intuitively clear axioms which are based on some intuition of Stuart Davidson and an old theorem of Sierpiński and are justified by the symmetry in a thought experiment throwing darts at the real number line. We will in fact show why there must be an infinity of cardinalities between the integers and the reals. We will also show why Martin's Axiom must be false, and we will prove the extension of Fubini's Theorem for Lebesgue measure where joint measurability is not assumed. Following the philosophy—if you reject CH you are only two steps away from rejecting the axiom of choice (AC)—we will point out along the way some extensions of our intuition which contradict AC.