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Transfinite Numbers and Cosmology

Naturevolume 193pages665666 (1962) | Download Citation



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.

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  1. 1

    Studium Generale, 5, 329 (1952).

  2. 2

    Bondi, H., and Gold, T., Mon. Not. Roy. Astro. Soc., 108, 252 (1948). Bondi, H., Cosmology, second ed., Chap. 12 (Cambridge, 1960).

  3. 3

    See, for example, Wilder, R. L., Introduction to the Foundations of Mathematics, Sec. 2, Chap. 4 (Wiley, New York, 1952).

  4. 4

    See, for example, Kleene, S. C., Introduction to Metamathematics, 4 (North-Holland Pub. Co., Amsterdam, 1952).

  5. 5

    Tolman, R. C., Relativity, Thermodynamics, and Cosmology, sec. 149 (Oxford, 1934).

  6. 6

    Kleene, S. C., Introduction to Metamathematics, 17 (North-Holland Pub. Co., Amsterdam, 1952).

  7. 7

    Hoyle, F., Mon. Not. Roy. Astro. Soc., 108, 372 (1948).

  8. 8

    Tolman, R. C., Relativity, Thermodynamics and Cosmology, secs. 142 and 158 (Oxford, 1934).

  9. 9

    Wilder, R. L., Introduction to the Foundations of Mathematics, 86 (Wiley, New York, 1952).

  10. 10

    Discussion and references are given by Schlegel, R., Amer. J. Phys., 26, 601 (1958).

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  1. History and Philosophy of Science, University of Cambridge, and Department of Physics, Michigan State University, East Lansing, Michigan



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