From Whole Numbers to Rational Numbers

  • Saunders Mac Lane


Various human activities such as listing, counting, and comparing lead, as we saw, to the natural numbers
$$ N = \{ 0,1,2,3,4, \ldots \} $$
and to the operations of addition, multiplication, and exponentiation on these numbers. These operations have a variety of general properties. For example, addition for all natural numbers k, m, and n satisfies the equations
$$ m + 0 = m,m + n = n + m, $$
$$ k + (m + n) = (k + m) + n. $$


Natural Number Arithmetic Operation Ordinal Number Order Type Cardinal Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag New York Inc. 1986

Authors and Affiliations

  • Saunders Mac Lane
    • 1
  1. 1.Department of MathematicsUniversity of ChicagoChicagoUSA

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