What are x and y?

  • Karl Menger


Consistent Classes of Quantities. An ordered pair whose second member (or value) is a number, while its first member (or object) may be anything, will be referred to as a quantity. By a consistent class of quantities—briefly, c.c.q. —we mean a class of quantities that does not contain two quantities with equal objects and unequal values. Reviving Newton’s term, we will refer to c.c.q.’s also as fluents. The class of all objects (of all values) of the quantities belonging to a fluent is called the domain (the range) of the fluent.


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  1. 1.
    This paper elaborates on ideas expressed in the Appendix to the author’s book Calculus. A Modern Approach, Ginn and Co., Boston 1955.Google Scholar
  2. 2.
    Where there is no indication to the contrary, “ number ” in this paper means real number.Google Scholar
  3. 3.
    Traditionally, x and y are printed in italic type as are all single letters used as mathematical symbols.Google Scholar
  4. 4.
    Cf. the author’s paper Random Variables and the General Theory of Variables to be published in the Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, University of California, 1955.Google Scholar
  5. 5.
    Since substitution of operators (universally denoted by mere juxtaposition) is often called multiplication, the identity operator j is usually denoted by 1.Google Scholar
  6. 6.
    After submitting the present paper, I found that Dr. I. T. A. C. Adamson (Mathematical Gazette, September 1955) has suggested a similar symbol for definite integrals in his interesting review of my 1953 notes on calculus, edited in a greatly enlarged and improved form in the book i.e.’.Google Scholar

Copyright information

© Springer-Verlag Wien 2003

Authors and Affiliations

  • Karl Menger
    • 1
  1. 1.Illinois Institute of TechnologyUSA

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