Journal of Symbolic Logic

Axioms of Symmetry: Throwing Darts at the Real Number Line

Chris Freiling

Full-text is available via JSTOR, for JSTOR subscribers. Go to this article in JSTOR.

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 Sierpinski 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.

Article information

Source
J. Symbolic Logic, Volume 51, Issue 1 (1986), 190-200.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183742039

Mathematical Reviews number (MathSciNet)
MR830085

Zentralblatt MATH identifier
0619.03035

JSTOR
links.jstor.org

Citation

Freiling, Chris. Axioms of Symmetry: Throwing Darts at the Real Number Line. J. Symbolic Logic 51 (1986), no. 1, 190--200. https://projecteuclid.org/euclid.jsl/1183742039


Export citation