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P-adic analysis
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===Ostrowski's theorem=== {{main article|Ostrowski's theorem}} Ostrowski's theorem, due to [[Alexander Ostrowski]] (1916), states that every non-trivial [[absolute value (algebra)|absolute value]] on the [[rational number]]s '''Q''' is equivalent to either the usual real absolute value or a [[p-adic number|{{mvar|p}}-adic]] absolute value.<ref>{{cite book |last=Koblitz |first=Neal |authorlink=Neal Koblitz |title=P-adic numbers, p-adic analysis, and zeta-functions |series=Graduate Texts in Mathematics |year=1984 |volume=58 |publisher=Springer-Verlag |location=New York |isbn=978-0-387-96017-3 |doi=10.1007/978-1-4612-1112-9 |edition=2nd |page=3 |quote='''Theorem 1''' (Ostrowski). Every nontrivial norm β β on <math>\mathbb{Q}</math> is equivalent to {{math|{{abs| }}<sub>''p''</sub>}} for some prime {{mvar|p}} or for {{math|1=''p'' = β}}.}}</ref>
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