“Don't hand that holier than thou line to me” is what the asymptote
said to the removable discontinuity.
The distance between the
curve and the line where it approaches zero as they tend to infinity is the line in the asymptote
of a curve. This is unusual for modern authors but in some
sources the requirement that the curve may not cross the line infinitely often
is included.
The point that does not fit the rest of the graph or is
undefined is called a removable discontinuity. By filling in a single
point, the removable discontinuity can be made connected.
