Show limit does not exist

Homework Statement

Show limit 1/x^2 when x approaches zero does not exist.

The Attempt at a Solution

What I do is suppose the limit exists,say L.Then I show that for all real number L, the limit does not approaches L. In this case, I separate L into different cases. Can anyone help me to check is this a valid prove.

$$\lim_{x \to 0}\frac{1}{x^2} = \infty$$