What is the difference between Undefined and Nonexistent Limits

[chez_butt23]

Homework Statement

I am having trouble understanding when limits are undefined and when they do not exist. I googled it and cannot find a good explanation. Can someone please explain this to me?

Homework Equations

The Attempt at a Solution

 

[gb7nash]

They're interchangeable as far as I know.

 

[Mark44]

Some examples might help.

Here's one where the limit does not exist.
$$\lim_{x \to 0} \frac{1}{x}$$

This limit doesn't exist because the left- and right-side limits aren't the same.

Here's one that's undefined.
$$\lim_{x \to 0} \frac{1}{x^2}$$
In this limit, the left-and right-side limits are the same, but are undefined, in the sense that infinity is not a number in the real number system.

That's how I would distinguish between these terms.

 

[chez_butt23]

Thank you. That helped a lot.