# Cauchy condition for limit of function

A real function $f$ has the limit $\underset{x\to {x}_{0}}{lim}f(x)$ if and only if for every positive number $\epsilon $ there exists another positive number $\delta (\epsilon )$ satisfying

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## References

- 1 Л. Д. Кудрявцев: Математический анализ. I том. Издательство ‘‘Высшая школа’’. Москва (1970).

Title | Cauchy condition for limit of function |
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Canonical name | CauchyConditionForLimitOfFunction |

Date of creation | 2013-03-22 17:42:18 |

Last modified on | 2013-03-22 17:42:18 |

Owner | pahio (2872) |

Last modified by | pahio (2872) |

Numerical id | 7 |

Author | pahio (2872) |

Entry type | Theorem |

Classification | msc 26B12 |

Classification | msc 26A06 |

Classification | msc 54E35 |

Synonym | necessary and sufficient condition of limit |

Related topic | Complete^{} |

Related topic | CauchyCriterionForTheExistenceOfALimitOfAFunction |