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- W36100467 abstract "This chapter discusses various approaches to the most important kind of numbers in all of mathematics, namely, the natural numbers. The inclusion of the number zero as the first one among the natural numbers is in accordance with the usage of most logicians, though many mathematicians do not include the number zero among the natural numbers but take the number one to be the first of these numbers. The natural numbers are the numbers used for counting things, where the things being counted are finitely many in number. The chapter also presents a certain well-known elementary axiomatic theory for the arithmetic of the natural numbers. The particular theory considered is the theory N or first-order Peano arithmetic. Its underlying logic is an elementary predicate logic with identity and operation symbols F°, in which the nonlogical constants are the following four constants: (1) 0, (2) S, (3) +, and (4) .. The first of these constants is an individual constant, the second is a singulary operation symbol, and the third and fourth are binary operation symbols." @default.
- W36100467 created "2016-06-24" @default.
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- W36100467 date "1971-01-01" @default.
- W36100467 modified "2023-09-25" @default.
- W36100467 title "THE NATURAL NUMBERS" @default.
- W36100467 doi "https://doi.org/10.1016/b978-0-7204-2098-2.50009-7" @default.
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