Nature Publishing Group, publisher of Nature, and other science journals and reference works nature about npg news@nature naturejobs natureevents help site index Nature my account e-alerts subscribe register SEARCH JOURNAL Saturday 27 September 2014 Journal Home Current Issue AOP Archive THIS ARTICLE Download PDF References Export citation Export references Send to a friend More articles like this Table of Contents < Previous | Next > Letters to Nature Nature 193, 665 - 666 (17 February 1962); doi:10.1038/193665a0 Transfinite Numbers and Cosmology RICHARD SCHLEGEL History and Philosophy of Science, University of Cambridge, and Department of Physics, Michigan State University, East Lansing, Michigan. THE steady-state cosmological theory of Bondi, Gold, and Hoyle implies that the number of atoms in the universe is infinite to an order equal to that of the power of the continuum. In contrast, I hope to show that for physical spaces of the kind that are normally considered in cosmology the number of atoms cannot be greater than a simple denumerable infinity. The question of the order of infinity of the number of galaxies or particles in the universe has previously been raised by G. J. Whitrow1. Studium Generale, 5, 329 (1952). Bondi, H. , and Gold, T. , Mon. Not. Roy. Astro. Soc., 108, 252 (1948). Bondi, H. , Cosmology, second ed., Chap. 12 (Cambridge, 1960). | ISI | See, for example, Wilder, R. L. , Introduction to the Foundations of Mathematics, Sec. 2, Chap. 4 (Wiley, New York, 1952). See, for example, Kleene, S. C. , Introduction to Metamathematics, 4 (North-Holland Pub. Co., Amsterdam, 1952). Tolman, R. C. , Relativity, Thermodynamics, and Cosmology, sec. 149 (Oxford, 1934). Kleene, S. C. , Introduction to Metamathematics, 17 (North-Holland Pub. Co., Amsterdam, 1952). Hoyle, F. , Mon. Not. Roy. Astro. Soc., 108, 372 (1948). | ISI | Tolman, R. C. , Relativity, Thermodynamics and Cosmology, secs. 142 and 158 (Oxford, 1934).
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