Abstract
For natural numbers we used the recursion theorem to define the arithmetic operations, and, subsequently, we proved that those operations are related to the operations of set theory in various desirable ways. Thus, for instance, we know that the number of elements in the union of two disjoint finite sets E and F is equal to #(E) + #(F). We observe now that this fact could have been used to define addition. If m and n are natural numbers, we could have defined their sum by finding disjoint sets E and F, with #(E) = m and #(F) = n, and writing m + n = #(E ∪ F).
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© 1974 Springer Science+Business Media New York
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Halmos, P.R. (1974). Ordinal Arithmetic. In: Naive Set Theory. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-1645-0_21
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DOI: https://doi.org/10.1007/978-1-4757-1645-0_21
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-90104-6
Online ISBN: 978-1-4757-1645-0
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