posted by Marcus .
A function can be continuous at every point of a deleted neighborhood of some point and still not have a limit at the point which is deleted.
I'm not even too sure what this means in calculus terms. Can you please explain it better? Thank you.
Consider f(x) = 1/x
f is continuous at every point in every neighborhood not including x=0.
Yet f does not have a limit at x=0; in fact it is not even defined at x=0.