Is the limit of 1/x^2 as x approaches 0 non-existent?

[JG89]

Obviously \lim_{x \rightarrow 0} \frac{1}{x^2} = \infty, but am I correct in saying that the limit as x approaches 0 of \frac{1}{x^2} doesn't exist?

If it did exist then one of the conditions would be, for values of x sufficiently close to 0, |x-\infty| = \infty < \delta which obviously isn't true for all positive values of delta. Am this correct?

 

[snipez90]

I think you are correct in saying that the limit does not exist. However,

\lim_{x \rightarrow a} f(x) = \infty means that for every N \in \Re there exists a number \delta > 0 such that, for all x,
if 0 < |x-a| < \delta, then f(x) > N.

 

[JG89]

I don't know how I made that mistake

Thanks for the reply though :)