Is an open circle a limit?
Nope. The open circle does mean the function is undefined at that particular x-value. However, limits do not care what is actually going on at the value. Limits only care about what happens as we approach it.
An open interval means boundary points are not included, and includes all real numbers of x for which . The notation for a closed interval uses parentheses: . Note: when graphing these, we use open circles.