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Principle of permanence : ウィキペディア英語版 | Principle of permanence
In mathematics, the principle of permanence is that a complex function (or functional equation) which is 0 on a set with a non-isolated point is 0 everywhere (or at least on the connected component of its domain which contains the point). There are various statements of the principle, depending on the type of function or equation considered. ==For a complex function of one variable== For one variable, the principle of permanence states that if ''f''(''z'') is an analytic function defined on an open connected subset ''U'' of the complex numbers C, and there exists a convergent sequence having a limit ''L'' which is in ''U'', such that ''f''(''a''''n'') = 0 for all ''n'', then ''f''(''z'') is uniformly zero on ''U''.〔'The Language of Science'', Tobias Dantzig, Joseph Mazur, and Barry Mazur, 2007, Penguin Books, pp. 98, 212.〕
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