Home/Differential Calculus/Limits/ε-δ definitionSection 2.2ε-δ definitionFormulavizCopy LaTeXlimx→af(x)=L⟺∀ε>0 ∃δ>0: 0<∣x−a∣<δ⇒∣f(x)−L∣<ε\lim_{x\to a}f(x)=L \quad\Longleftrightarrow\quad \forall\varepsilon>0\ \exists\delta>0:\ 0<|x-a|<\delta\Rightarrow|f(x)-L|<\varepsilonx→alimf(x)=L⟺∀ε>0 ∃δ>0: 0<∣x−a∣<δ⇒∣f(x)−L∣<εFormal definition of a finite limit.⟺\Longleftrightarrow⟺∀ε>0 ∃δ>0: 0<∣x−a∣<δ⇒∣f(x)−L∣<ε\forall\varepsilon>0\ \exists\delta>0:\ 0<|x-a|<\delta\Rightarrow|f(x)-L|<\varepsilon∀ε>0 ∃δ>0: 0<∣x−a∣<δ⇒∣f(x)−L∣<εView detail →
FormulavizCopy LaTeXlimx→af(x)=L⟺∀ε>0 ∃δ>0: 0<∣x−a∣<δ⇒∣f(x)−L∣<ε\lim_{x\to a}f(x)=L \quad\Longleftrightarrow\quad \forall\varepsilon>0\ \exists\delta>0:\ 0<|x-a|<\delta\Rightarrow|f(x)-L|<\varepsilonx→alimf(x)=L⟺∀ε>0 ∃δ>0: 0<∣x−a∣<δ⇒∣f(x)−L∣<εFormal definition of a finite limit.⟺\Longleftrightarrow⟺∀ε>0 ∃δ>0: 0<∣x−a∣<δ⇒∣f(x)−L∣<ε\forall\varepsilon>0\ \exists\delta>0:\ 0<|x-a|<\delta\Rightarrow|f(x)-L|<\varepsilon∀ε>0 ∃δ>0: 0<∣x−a∣<δ⇒∣f(x)−L∣<εView detail →