Abstract
The introduction of addition for natural numbers is a typical example of definition by induction. Indeed, it follows from the recursion theorem that for each natural number m there exists a function s m from ω to ω such that s m (0) = m and such that s m (n +) = (s m (n))+ for every natural number n; the value s m (n) is, by definition, the sum m + n. The general arithmetic properties of addition are proved by repeated applications of the principle of mathematical induction. Thus, for instance, addition is associative.
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© 1974 Springer Science+Business Media New York
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Halmos, P.R. (1974). Arithmetic. In: Naive Set Theory. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-1645-0_13
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DOI: https://doi.org/10.1007/978-1-4757-1645-0_13
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-90104-6
Online ISBN: 978-1-4757-1645-0
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