翻訳と辞書
Words near each other
・ Principle of least interest
・ Principle of least motion
・ Principle of least privilege
・ Principle of locality
・ Principle of marginality
・ Principle of material objectivity
・ Principle of maximum entropy
・ Principle of maximum work
・ Principle of minimum energy
・ Principle of no-work-no-pay (dies non)
・ Principle of nonvacuous contrast
・ Principle of normality
・ Principle of opportunity
・ Principle of original horizontality
・ Principle of orthogonal design
Principle of permanence
・ Principle of plenitude
・ Principle of Priority
・ Principle of rationality
・ Principle of relativity
・ Principle of restricted choice
・ Principle of similitude
・ Principle of sufficient reason
・ Principle of transformation groups
・ Principle of Typification
・ Principle of Ubiquity
・ Principle of Univariance
・ Principle value
・ Principle-policy puzzle
・ Principled Distance


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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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