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| Pole DC | Wartość | Język |
|---|---|---|
| dc.contributor.author | Watase, Yasushige | pl |
| dc.date.accessioned | 2016-12-15T13:01:50Z | - |
| dc.date.available | 2016-12-15T13:01:50Z | - |
| dc.date.issued | 2015 | pl |
| dc.identifier.citation | Formalized Mathematics, Volume 23, Issue 2, 101–106 | pl |
| dc.identifier.issn | 1426-2630 | pl |
| dc.identifier.issn | 1898-9934 | pl |
| dc.identifier.uri | http://hdl.handle.net/11320/4874 | - |
| dc.description.abstract | AbstractIn this article we formalize some results of Diophantine approximation, i.e. the approximation of an irrational number by rationals. A typical example is finding an integer solution (x, y) of the inequality |xθ − y| ≤ 1/x, where 0 is a real number. First, we formalize some lemmas about continued fractions. Then we prove that the inequality has infinitely many solutions by continued fractions. Finally, we formalize Dirichlet’s proof (1842) of existence of the solution [12], [1]. | pl |
| dc.language.iso | en | pl |
| dc.publisher | De Gruyter Open | pl |
| dc.subject | irrational number | pl |
| dc.subject | approximation | pl |
| dc.subject | continued fraction | pl |
| dc.subject | rational number | pl |
| dc.subject | Dirichlet’s proof | pl |
| dc.title | Introduction to Diophantine Approximation | pl |
| dc.type | Article | pl |
| dc.identifier.doi | 10.1515/forma-2015-0010 | pl |
| dc.description.Affiliation | Suginami-ku Matsunoki 6, 3-21 Tokyo, Japan | pl |
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| Występuje w kolekcji(ach): | Formalized Mathematics, 2015, Volume 23, Issue 2 | |
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