Does Not Exist

The formal definition for does not exist is: $\exists ϵ>0$ s.t $\forall \delta \in R$, $\exists x\in R$ s.t $0<|x-c|<\delta$ and $|h(x)-L|\ge ϵ$ Alternatively, you can intuit it as: $\forall L\in R,{\lim }_{x\to c}h(x)\ne L$

Proof Process

1. Choose $ϵ=???$ (Note $ϵ>0$)
2. Let $\delta >0$ be arbitrary
3. Let $x_1,x_2\in I$ where

Occurrences

• Occurs at oscillating values, infinities and x/0.