From Whole Numbers to Rational Numbers

Saunders Mac Lane
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Saunders Mac Lane: University of Chicago, Department of Mathematics

Chapter Chapter II in Mathematics Form and Function, 1986, pp 42-60 from Springer

Abstract: Abstract 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 (1) $$ m + 0 = m,m + n = n + m, $$ (2) $$ k + (m + n) = (k + m) + n. $$

Keywords: Natural Number; Arithmetic Operation; Ordinal Number; Order Type; Cardinal Number (search for similar items in EconPapers)
Date: 1986
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DOI: 10.1007/978-1-4612-4872-9_3

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