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Ostrowski's Theorem
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Geliefert zwischen Fr., 30.01.2026 und Mo., 02.02.2026
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Ostrowski''s theorem, due to Alexander Ostrowski, states that any non-trivial absolute value on the rational numbers Q is equivalent to either the usual real absolute value or a p-adic absolute value. Since is non-Archimedean, n 1 for all integers n. Also as is non-trivial, there exists an integer n such that n 1 and n = p1^{e1} ldots pr^{er} by integer factorization. From this, we can deduce p 1 for some prime p. Suppose for contradiction p, q are distinct primes with p , q 1. Pick e, f such that p e, q f 1 and write 1 = rpe + sqf for some integers r, s by Bézout''s identity. But then 1 = rpe + sqf max( r , s ) 1, which is a desired contradiction. So must have p = , some 0 1, and q = 1 for all other primes q. Therefore is equivalent to the p-adic absolute value.
Weitere Informationen
- Allgemeine Informationen
- GTIN 09786131298370
- Editor Lambert M. Surhone, Mariam T. Tennoe, Susan F. Henssonow
- Größe H220mm x B220mm
- EAN 9786131298370
- Format Fachbuch
- Titel Ostrowski's Theorem
- Herausgeber Betascript Publishing
- Anzahl Seiten 104
- Genre Mathematik
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