Erschienen in:

2004 | OriginalPaper | Buchkapitel

Limits and the Continuity of Functions

verfasst von : Steven G. Krantz

Erschienen in: A Handbook of Real Variables

Verlag: Birkhäuser Boston

Enthalten in: Professional Book Archive

Zugang erhalten

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Definition 5.1 Let E ℝ be a set and let f be a real-valued function with domain E. Fix a point P∈ ℝ that is either in E or is an accumulation point of E. We say that f has limit l at P, and we write $$ \mathop {\lim }\limits_{E \mathrel\backepsilon x \to P} f(x) = \ell ,$$ with l a real number, if for each ∈ > 0 there is a δ > 0 such that when x ∈ E and 0 <-P< δ then $$ |f(x) - \ell | < \in .$$

Springer Professional