This is yet another instance of
a function being not continuous at x = 0 Naively, we may say that a function is
continuous at a fixed point if we can draw the
graph of the function around that point without
lifting the pen from the plane of the paper Mathematically, it may be phrased precisely as follows:
Definition 1 Suppose f is a real function on a subset of the real numbers and let  c be
a point in the domain of f Then f is continuous at c if
lim
( )
( )
x
c f x
f c
→
=
More elaborately, if the left hand limit, right hand limit and the value of the function
at x = c exist and equal to each other, then f is said to be continuous at x = c