Cauchy condition for limit of function

A real function f has the limit limxx0f(x) if and only if for every positive number ε there exists another positive number δ(ε) satisfying

|f(u)-f(v)|<εwhen0<|u-x0|<δ(ε)and  0<|v-x0|<δ(ε).


  • 1 Л. Д. Кудрявцев: Математический анализ. I том.  Издательство  ‘‘Высшая школа’’. Москва (1970).
Title Cauchy condition for limit of function
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 CompletePlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath
Related topic CauchyCriterionForTheExistenceOfALimitOfAFunction