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Formal Number Theory
| Content Provider | Scilit |
|---|---|
| Author | Mendelson, Elliott |
| Copyright Year | 2015 |
| Description | Together with geometry, the theory of numbers is the most immediately intuitive of all branches of mathematics. It is not surprising, then, that attempts to formalize mathematics and to establish a rigorous foundation for mathematics should begin with number theory. The ˆrst semiaxiomatic presentation of this subject was given by Dedekind in 1879 and, in a slightly modiˆed form, has come to be known as Peano's postulates.* It can be formulated as follows: (P1) 0 is a natural number.† (P2) If x is a natural number, there is another natural number denoted by x′ (and called the successor of x).‡ (P3) 0 ≠ x′ for every natural number x. (P4) If x′ = y′, then x = y. (P5) If Q is a property that may or may not hold for any given natural number, and if (I) 0 has the property Q and (II) whenever a natural number x has the property Q, then x′ has the property Q, then all natural numbers have the property Q (mathematical induction principle). Book Name: Introduction to Mathematical Logic |
| Related Links | https://content.taylorfrancis.com/books/download?dac=C2015-0-75583-4&isbn=9780429162091&doi=10.1201/b18519-6&format=pdf |
| Ending Page | 254 |
| Page Count | 78 |
| Starting Page | 177 |
| DOI | 10.1201/b18519-6 |
| Language | English |
| Publisher | Informa UK Limited |
| Publisher Date | 2015-05-21 |
| Access Restriction | Open |
| Subject Keyword | Book Name: Introduction to Mathematical Logic History and Philosophy of Science Number Theory |
| Content Type | Text |
| Resource Type | Chapter |
