# Showing a limit doesn't exist using Delta/Epsilon

lepton123

## Homework Statement

Prove that the limit as x approaches 0 of 1/x does not exist

## Homework Equations

Delta epsilon definition

## The Attempt at a Solution

I'm really stuck

mtayab1994
Use the following definition:

$$\forall L;\exists\epsilon>0;\forall\delta>0;\exists x:|x-a|<\delta and|f(x)-L|<\epsilon$$

lepton123
I know that is the definition for a limit, but I am unsure how to disprove it

mtayab1994
Well first assume that : $$\lim_{x\rightarrow0}\frac{1}{x}=L$$

Mentor
lepton123,
Please read your private mails. You have started two threads without showing any effort. If you continue doing so, it could result in a ban from this forum.

mtayab,
Please, no more hints until lepton123 shows some effort.